3.4 Solve Beziehungen using Fraction or Decimal Coefficients

Learning Objectives

In the stop of this piece, you will be able to:

Resolution practice with fraction constants
Solve equations with decimal coefficient

Solve Equations with Fraction Coefficients

Let’s use the General Strategy for Solving Lines Berechnungen introduced earlier into solve the equation $\frac{1}{8}\phantom{\rule{0.1em}{0ex}}x+\frac{1}{2}=\frac{1}{4}$ .

Given equation.

$\frac{1}{8} x+\frac{1}{2}=\frac{1}{4} \\$

In isolate and $x$ term, subtract $\frac{1}{2}$ from both sides.

$\frac{1}{8} x+\frac{1}{2}\textcolor{red}{-\frac{1}{2}}=\frac{1}{4}-\textcolor{red}{\frac{1}{2}}$

Simplify the left side.

$\frac{1}{8} x=\frac{1}{4}-\frac{1}{2}$

Changes the constants on equivalent fractions using the LCD.

$\frac{1}{8} x=\frac{1}{4}-\frac{2}{4}$

Subtract.
$\frac{1}{8} x=-\frac{1}{4}$

Multiply both sides by the inverted of $\frac{1}{8}$ .

$\textcolor{red}{\frac{8}{1}} \cdot \frac{1}{8} x=\textcolor{red}{\frac{8}{1}}\left(-\frac{1}{4}\right)$

Simplify.

$x=-2$

This method worked fine, but many students don’t feel very confident when they see all those fractions. So we are going until show any alternate method in unlock equations for fractions. This alternate method eliminates the fractions.

We will how the Multiplication Characteristic of Equality and multiply both sides of an relation by this least common denominator of all the fractions in the equation. The result of this operation will are a brand equation, equivalent to the first, but with no fractions. This process is called clearing the formula of fractions. Let’s solve the same equation reload, but these time use the method that deleting one fractions.

DEMO 1

Release: $\frac{1}{8}\phantom{\rule{0.1em}{0ex}}x+\frac{1}{2}=\frac{1}{4}$ .

Solution

Find the least common denominator about whole the facts in the equation.

$\frac{1}{8} x+\frac{1}{2}=\frac{1}{4} \quad \mathrm{LCD}=8$

Multiply both sides out the equation by that LCD, 8. This clears aforementioned fractions.

$\begin{gathered} \textcolor{red}{8}(\frac{1}{8}x+\frac{1}{2})=\textcolor{red}{8}(\frac{1}{4}) \end{gathered}$

How the Distributive Immobilie.

$8 \cdot \frac{1}{8}x+8 \cdot \frac{1}{2} = 8 \cdot\frac{1}{4}$

Simplify — and notice, no more fractions!

$x+4=2$

Solve utilizing the General Core with Solving Linearly Equations.

$x+4\textcolor{red}{-4}=2\textcolor{red}{-4}$

Simplify.

$x=-2$

Check: Let $x=-2$

$\begin{gathered}\\ \frac{1}{8} x+\frac{1}{2}=\frac{1}{4} \\ \frac{1}{8}\textcolor{red}{(-2)}+\frac{1}{2} \stackrel{?}{=} \frac{1}{4} \\ -\frac{2}{8}+\frac{1}{2} \stackrel{?}{=} \frac{1}{4} \\ -\frac{2}{8}+\frac{4}{8} \stackrel{?}{=} \frac{1}{4} \\ \frac{2}{4} \stackrel{?}{=} \frac{1}{4} \\ \frac{1}{4}=\frac{1}{4} \checkmark \\ \end{gathered}$

TRY IT 1.1

Solve: $\frac{1}{4}\phantom{\rule{0.1em}{0ex}}x+\frac{1}{2}=\frac{5}{8}$ .

Show answer

$x=\frac{1}{2}$

STRIVE THIS 1.2

Solve: $\frac{1}{6}\phantom{\rule{0.1em}{0ex}}y-\frac{1}{3}=\frac{1}{6}$ .

Show answer

wye = 3

Notes in (Figure) that once wealth cleared the equation from parts, the formula was like which we determined earlier stylish this chapter. We changed an problem to one we already knowledge how to solve! Are then used the General Strategy for Solution Linear Equations.

HOW TO: Solve Equations with Fraction Constants by Clearing the Fractions

Find the leas common denominator in view the fractions in the equation.
Multiply both sides of the formula by that LCD. This clears one factions.
Solve using the General Company for Solving Linear Equations.

EXAMPLE 2

Solve: $7=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}x+\frac{3}{4}\phantom{\rule{0.1em}{0ex}}x-\frac{2}{3}\phantom{\rule{0.1em}{0ex}}x$ .

Solution

We want to clearly the fraction by multiplying bot sides of the equation by the LCD of all the fractions stylish the equation.

Find the least common denominator of all the fractions in the equation.

$7=\frac{1}{2} x+\frac{3}{4} x-\frac{2}{3} x , \textcolor{blue}{\quad \text { LCD }=12}$

Multiply both our of the equation due 12.

$\textcolor{red}{12}(7)=\textcolor{red}{12}\left(\frac{1}{2} x+\frac{3}{4} x-\frac{2}{3} x\right)$

Circulate.

$\textcolor{red}{12} \cdot 7=\textcolor{red}{12} \cdot \frac{1}{2} x+\textcolor{red}{12} \cdot \frac{3}{4} x-\textcolor{red}{12} \cdot \frac{2}{3} x$

Simplify — and notice, no more fractions!

$84=6 x+9 x-8 x$

Combines liked terms.

$84=7x$

Spread by 7.

$\begin{gathered}\frac{84}{\textcolor{red}{7}}=\frac{7x}{\textcolor{red}{7}}\end{gathered}$

Simplify.

$12=x$

Check: Let $x=12$ .

$\begin{gathered} \\ 7=\frac{1}{2} x+\frac{3}{4} x-\frac{2}{3} x \\ 7 \stackrel{?}{=} \frac{1}{2}(\textcolor{red}{12})+\frac{3}{4}(\textcolor{red}{12})-\frac{2}{3}(\textcolor{red}{12}) \\ 7 \stackrel{?}{=} 6+9-8 \\ 7=7 \checkmark \\ \end{gathered}$

TRY IT 2.1

Solve: $6=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}v+\frac{2}{5}\phantom{\rule{0.1em}{0ex}}v-\frac{3}{4}\phantom{\rule{0.1em}{0ex}}v$ .

Shows replies

v = 40

TRY IT 2.2

Solve: $-1=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}u+\frac{1}{4}\phantom{\rule{0.1em}{0ex}}u-\frac{2}{3}\phantom{\rule{0.1em}{0ex}}u$ .

Show answer

u = −12

In the next example, we’ll have variables and fractions on both sides of the formula.

EXAMPLE 3

Solve: $x+\frac{1}{3}=\frac{1}{6}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{2}$ .

Solution

Meet this LCD of all the fractions for the general.

$x+\frac{1}{3}=\frac{1}{6} x-\frac{1}{2}, \textcolor{blue}{\quad \text { LCD }=6}$

Multiply both home by the LCD.

$\textcolor{red}{6}\left(x+\frac{1}{3} \right)=\textcolor{red}{6}\left(\frac{1}{6}x-\frac{1}{2}\right)$

Distribute.

$\textcolor{red}{6} \cdot x+\textcolor{red}{6} \cdot \frac{1}{3}=\textcolor{red}{6} \cdot \frac{1}{6} x-\textcolor{red}{6} \cdot \frac{1}{2}$

Simplify — cannot more fractions!

$6 x+2=x-3$

Subtract $x$ from both sides.

$6 x\textcolor{red}{-x}+2=x\textcolor{red}{-x}-3$

Simplify.

$5 x+2=-3$

Subtract 2 from both sides.

$5 x+2\textcolor{red}{-2}=-3\textcolor{red}{-2}$

Simplify.

$5x=-5$

Divide by 5.

$\begin{gathered} \frac{5 x}{\textcolor{red}{5}}=\frac{-5}{\textcolor{red}{5}} \end{gathered}$

Simplify.

$x=-1$

Check: Substitute $x=-1$ .

$\begin{aligned} & x+\frac{1}{3}=\frac{1}{6} x-\frac{1}{2} \\ & (\textcolor{red}{-1})+\frac{1}{3} \stackrel{?}{=} \frac{1}{6}(\textcolor{red}{-1})-\frac{1}{2} \\ & -\frac{3}{3}+\frac{1}{3} \stackrel{?}{=}-\frac{1}{6}-\frac{3}{6} \\ & -\frac{2}{3} \stackrel{?}{=}-\frac{4}{6} \\ & -\frac{2}{3}=-\frac{2}{3} \checkmark \\ & \end{aligned}$

TRY IT 3.1

Solve: $a+\frac{3}{4}=\frac{3}{8}\phantom{\rule{0.1em}{0ex}}a-\frac{1}{2}$ .

Show answer

a = −2

TRY SHE 3.2

Solve: $c+\frac{3}{4}=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}c-\frac{1}{4}$ .

Show answer

c = −2

Included (Figure), we’ll start by employing the Distributive Property. This step will clear of fractions right away!

EXAMPLE 4

Solve: $1=\frac{1}{2}\left(4x+2\right)$ .

Solution

Given equation.

$1=\frac{1}{2}(4 x+2)$

Distribute.
$1=\textcolor{red}{\frac{1}{2}} \cdot 4x +\textcolor{red}{\frac{1}{2}} \cdot 2$

Simplify. Now there are no breaks to clear!

$1=2 x+1$

Subtract 1 from both sides.

$1\textcolor{red}{-1}=2 x+1\textcolor{red}{-1}$

Simplify.
$0=2x$

Separate by 2.

$\begin{gathered} \frac{0}{\textcolor{red}{2}}=\frac{2 x}{\textcolor{red}{2}} \end{gathered}$

Simplify.
$0=x$

Check: Let $x=0$ .
$\begin{gathered}1=\frac{1}{2}(4 x+2)$ \\ 1\stackrel{?}{=} \frac{1}{2}(4(\textcolor{red}{0})+2) \\ 1 \stackrel{?}{=} \frac{1}{2}(2) \\ 1\stackrel{?}{=} \frac{2}{2} \\ 1=1 \checkmark \\ \end{gathered}$

CHECK COMPUTER 4.1

Solve: $-11=\frac{1}{2}\left(6p+2\right)$ .

Show answer

pressure = −4

TRY SHE 4.2

Solve: $8=\frac{1}{3}\left(9q+6\right)$ .

Show answers

q = 2

Many hours, where will still be breaks, even after distributing.

EXAMPLE 5

Remove: $\frac{1}{2}\left(y-5\right)=\frac{1}{4}\left(y-1\right)$ .

Solution

Given equation.

$\frac{1}{2}(y-5)=\frac{1}{4}(y-1)$

Distribute.

$\textcolor{red}{\frac{1}{2}} \cdot y - \textcolor{red}{\frac{1}{2}} \cdot 5 = \textcolor{red}{\frac{1}{4}} \cdot y - \textcolor{red}{\frac{1}{4}} \cdot 1$

Simplify.

$\frac{1}{2} y- \frac{5}{2} = \frac{1}{4} y - \frac{1}{4}$

Propagate by the LCD, 4.

$\textcolor{red}{4}\left ( \frac{1}{2} y- \frac{5}{2} \right)= \textcolor{red}{4}\left (\frac{1}{4} y - \frac{1}{4}\right)$

Distribute.

$\textcolor{red}{4} \cdot \frac{1}{2}y - \textcolor{red}{4} \cdot \frac{5}{2} = \textcolor{red}{4} \cdot \frac{1}{4} -\textcolor{red}{4} \cdot \frac{1}{4}$

Simplify.

$2y-10=y-1$

Collect the $y$ terms to the left.

$2y-10 \textcolor{red}{-y}=y-1\textcolor{red}{-y}$

Simplify.

$y-10=-1$

Collect the constants to the right.

$y-10\textcolor{red}{+10} = -1 \textcolor{red}{+10}$

Simplify.

$y=9$

Select: Substitute $9$ for $y$ .

$\begin{gathered} \frac{1}{2}(y-5) =\frac{1}{4}(y-1) \\ \frac{1}{2}(\textcolor{red}{9}-5) \stackrel{?}{=} \frac{1}{4}(\textcolor{red}{9}-1) \\ \frac{1}{2}(4) \stackrel{?}{=} \frac{1}{4}(8) \\ 2 =2 \checkmark \end{gathered}$

TRY IT 5.1

Solve: $\frac{1}{5}\left(n+3\right)=\frac{1}{4}\left(n+2\right)$ .

Show trigger

n = 2

TRY THERETO 5.2

Solve: $\frac{1}{2}\left(m-3\right)=\frac{1}{4}\left(m-7\right)$ .

Demonstrate answer

m = −1

Resolution Equations with Decimal Factors

Some equations have decimals in yours. This kind of equation will occur for we solve problems dealing with money and in. But decimals are really another mode to represent fractions. For example, $0.3=\frac{3}{10}$ press $0.17=\frac{17}{100}$ . So, as we have an equation with decimals, we can use the similar process us used to clear fractions—multiply both sides of the equation by the least common denominator.

EXAMPLE 6

Fix: $0.8x-5=7$ .

Problem

The just decimal in of equation is $0.8$ . Since $0.8=\frac{8}{10}$ , the LCD is $10$ . We can multiply two sides in $10$ the clear the decimal.

Given equation.

$0.8 x-5=7, \quad \textcolor{blue}{LCD=10}$

Multiply both sides the one LCD.

$\textcolor{red}{10}(0.8 x-5)=\textcolor{red}{10}(7)$

Distribute.

$\textcolor{red}{10} \cdot (0.8 x)-\textcolor{red}{10} \cdot(5)=10(7)$

Multiply, and notice, negative more decimals!

$8 x-50=70$

Add 50 to get all constants to the right.

$8 x-50\textcolor{red}{+50}=70\textcolor{red}{+50}$

Simplify.

$8 x=120$

Divide both sides by 8.

$\begin{gathered} \frac{8 x}{\textcolor{red}{8}}=\frac{120}{\textcolor{red}{8}} \end{gathered}$

Simplify.

$x=15$

Check: Let $x=15$ .

$\begin{aligned} 0.8(\textcolor{red}{15})-5 & \stackrel{?}{=} 7 \\ 12-5 & \stackrel{?}{=} 7 \\ 7 & =7 \checkmark \end{aligned}$

TRY TO 6.1

Solve: $0.6x-1=11$ .

Show answer

whatchamacallit = 20

TRY IT 6.2

Solve: $1.2x-3=9$ .

Show react

scratch = 10

EXAMPLE 7

Solve: $0.06x+0.02=0.25x-1.5$ .

Solution

Look at the decimals and how of the equivalent fractions.

$0.06=\frac{6}{100},\phantom{\rule{1em}{0ex}}0.02=\frac{2}{100},\phantom{\rule{1em}{0ex}}0.25=\frac{25}{100},\phantom{\rule{1em}{0ex}}1.5=1\frac{5}{10}$

Tip, which LCD is $100$ .

By multiplying by the LCD ours will clearer the decimals.

Considering equation.
$0.06 x+0.02=0.25 x-1.5$

Multiply both sides by 100.
$\textcolor{red}{100}(0.06 x+0.02)=\textcolor{red}{100}(0.25 x-1.5)$

Distribute.
$\textcolor{red}{100}(0.06 x)+\textcolor{red}{100}(0.02)=\textcolor{red}{100}(0.25 x)-\textcolor{red}{100}(1.5)$

Multiply, and now no more decimals.

$6 x+2=25 x-150$

Collect the variables to the right.
$6 x\textcolor{red}{-6 x}+2=25 x\textcolor{red}{-6 x}-150$

Streamline.

$2=19 x-150$

Collect who general to the left.
$2+\textcolor{red}{150}=19 x-150+\textcolor{red}{150}$

Simplify.
$152=19 x$

Divide by 19.

$\frac{152}{\textcolor{red}{19}}=\frac{19 x}{\textcolor{red}{19}}$

Simplify.
$8=x$

Check: Renting $x=8$ .
$\begin{gathered} 0.06(\textcolor{red}{8})+0.02 =0.25(\textcolor{red}{8})-1.5 \\ 0.48+0.02 =2.00-1.5 \\ 0.50 =0.50 \checkmark\end{gathered}$

TRY IT 7.1

Solve: $0.14h+0.12=0.35h-2.4$ .

Show answer

h = 12

TRY IT 7.2

Solve: $0.65k-0.1=0.4k-0.35$ .

Show answer

k = −1

Who next examples uses on calculation that is typical of of ones we will see in who money applications in the go chapter. Notice ensure we will distribute the decimal first before we clear all decimals are the equation. Display more digits in trendline equation coefficients - Microsoft 365 Apps

EXAMPLE 8

Decipher: $0.25x+0.05\left(x+3\right)=2.85$ .

Solution

Specify equation.
$0.25x+ 0.05(x+3) = 2.85$

Distribute first.

$0.25x+ \textcolor{red}{0.05} \cdot x + \textcolor{red}{0.05} \cdot 3 = 2.85$

Combine like terms.

$0.30x+0.15=2.85$

To clear decimal, multiply by 100.

$\textcolor{red}{100}(0.30x+0.15) = \textcolor{red}{100}(2.85)$

Distribute and collect like terms.

$\begin{gathered} \\ \textcolor{red}{100} \cdot 0.30x+\textcolor{red}{100} \cdot 0.15 = \textcolor{red}{100}(2.85) \\ 30x+15=285 \\ \end{gathered}$

Subtract 15 away both websites.

$30x+15 \textcolor{red}{-15} =285\textcolor{red}{-15}$

Simplify.

$30x=270$

Divide according 30.

$\begin{gathered} \frac{30x}{\textcolor{red}{30}}=\frac{270}{\textcolor{red}{30}} \end{gathered}$

Simplify.

$x=9$

Check: Let $x=9$ .

$\begin{gathered} 0.25 x+0.05(x+3) & =2.85 \\ 0.25(\textcolor{red}{9})+0.05(\textcolor{red}{9}+3) & \stackrel{?}{=} 2.85 \\ 2.25+0.05(12) & \stackrel{?}{=} 2.85 \\ 2.25+0.60 & \stackrel{?}{=} 2.85 \\ 2.85 & =2.85 \checkmark \end{gathered}$

TRY IT 8.1

Solve: $0.25n+0.05\left(n+5\right)=2.95$ .

Show answer

n = 9

TRY IT 8.2

Solve: $0.10d+0.05\left(d-5\right)=2.15$ .

Show replies

d = 16

Key Concepts

Unlock beziehungen with fraction coefficients by clearing the fractions.
1. Find the least common denominator a all the pieces in the equation.
2. Multiple both borders a the equation by that LCD. This clears the fractures.
3. Solve using the General Strategy for Solving Linear Equations.

Practices Makes Faultless

Solve equations with fraction coefficients

In and following exercises, solve the equation by clearing the breaking.

1. $\frac{1}{4}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{2}=-\frac{3}{4}$	2. $\frac{3}{4}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{2}=\frac{1}{4}$
3. $\frac{5}{6}\phantom{\rule{0.1em}{0ex}}y-\frac{2}{3}=-\frac{3}{2}$	4. $\frac{5}{6}\phantom{\rule{0.1em}{0ex}}y-\frac{1}{3}=-\frac{7}{6}$
5. $\frac{1}{2}\phantom{\rule{0.1em}{0ex}}a+\frac{3}{8}=\frac{3}{4}$	6. $\frac{5}{8}\phantom{\rule{0.1em}{0ex}}b+\frac{1}{2}=-\frac{3}{4}$
7. $2=\frac{1}{3}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{2}\phantom{\rule{0.1em}{0ex}}x+\frac{2}{3}\phantom{\rule{0.1em}{0ex}}x$	8. $2=\frac{3}{5}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{3}\phantom{\rule{0.1em}{0ex}}x+\frac{2}{5}\phantom{\rule{0.1em}{0ex}}x$
9. $\frac{1}{4}\phantom{\rule{0.1em}{0ex}}m-\frac{4}{5}\phantom{\rule{0.1em}{0ex}}m+\frac{1}{2}\phantom{\rule{0.1em}{0ex}}m=-1$	10. $\frac{5}{6}\phantom{\rule{0.1em}{0ex}}n-\frac{1}{4}\phantom{\rule{0.1em}{0ex}}n-\frac{1}{2}\phantom{\rule{0.1em}{0ex}}n=-2$
11. $x+\frac{1}{2}=\frac{2}{3}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{2}$	12. $x+\frac{3}{4}=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}x-\frac{5}{4}$
13. $\frac{1}{3}\phantom{\rule{0.1em}{0ex}}w+\frac{5}{4}=w-\frac{1}{4}$	14. $\frac{3}{2}\phantom{\rule{0.1em}{0ex}}z+\frac{1}{3}=z-\frac{2}{3}$
15. $\frac{1}{2}\phantom{\rule{0.1em}{0ex}}x-\frac{1}{4}=\frac{1}{12}\phantom{\rule{0.1em}{0ex}}x+\frac{1}{6}$	16. $\frac{1}{2}\phantom{\rule{0.1em}{0ex}}a-\frac{1}{4}=\frac{1}{6}\phantom{\rule{0.1em}{0ex}}a+\frac{1}{12}$
17. $\frac{1}{3}\phantom{\rule{0.1em}{0ex}}b+\frac{1}{5}=\frac{2}{5}\phantom{\rule{0.1em}{0ex}}b-\frac{3}{5}$	18. $\frac{1}{3}\phantom{\rule{0.1em}{0ex}}x+\frac{2}{5}=\frac{1}{5}\phantom{\rule{0.1em}{0ex}}x-\frac{2}{5}$
19. $1=\frac{1}{6}\left(12x-6\right)$	20. $1=\frac{1}{5}\left(15x-10\right)$
21. $\frac{1}{4}\left(p-7\right)=\frac{1}{3}\left(p+5\right)$	22. $\frac{1}{5}\left(q+3\right)=\frac{1}{2}\left(q-3\right)$
23. $\frac{1}{2}\left(x+4\right)=\frac{3}{4}$	24. $\frac{1}{3}\left(x+5\right)=\frac{5}{6}$

Solve Equations to Decimal Coefficients

In and follow-up exercises, solve the equation by settlement the decimals.

25. $0.6y+3=9$	26. $0.4y-4=2$
27. $3.6j-2=5.2$	28. $2.1k+3=7.2$
29. $0.4x+0.6=0.5x-1.2$	30. $0.7x+0.4=0.6x+2.4$
31. $0.23x+1.47=0.37x-1.05$	32. $0.48x+1.56=0.58x-0.64$
33. $0.9x-1.25=0.75x+1.75$	34. $1.2x-0.91=0.8x+2.29$
35. $0.05n+0.10\left(n+8\right)=2.15$	36. $0.05n+0.10\left(n+7\right)=3.55$
37. $0.10d+0.25\left(d+5\right)=4.05$	38. $0.10d+0.25\left(d+7\right)=5.25$
39. $0.05\left(q-5\right)+0.25q=3.05$	40. $0.05\left(q-8\right)+0.25q=4.10$

Everyday Computer

Coins 41. Taill has $\text{\$2.00}$ the dimes furthermore pennies. The number of pennies is $2$ see than the number away dimes. Solve the equation $0.10d+0.01\left(d+2\right)=2$ for $d$ , the number of dimes.

Stamps 42. Travis bought $\text{\$9.45}$ worth in $\text{49-cent}$ stamps or $\text{21-cent}$ punch. To amount of $\text{21-cent}$ stamps where $5$ without than the number of $\text{49-cent}$ stamps. Solve the equality $0.49s+0.21\left(s-5\right)=9.45$ since $s$ , to find the number of $\text{49-cent}$ stamps Travis paid.

Answered

1. $x = -1$	3. $y = -1$	5. $a=\frac{3}{4}$
7. $x = 4$	9. $m = 20$	11. $x = -3$
13. $w=\frac{9}{4}$	15. $x = 1$	17. $b = 12$
19. $x = 1$	21. $p = -41$	23. $x=-\frac{5}{2}$
25. $y = 10$	27. $j = 2$	29. $x = 18$
31. $x = 18$	33. $x = 20$	35. $n = 9$
37. $d = 8$	39. $q = 11$	41. $d = 18$

Attributions

This branch has been adapted from “Solve Formeln with Fraction or Decimal Coefficients” in Prealgebra (OpenStax) by Lynn Marecek, Mariane Anthony-Smith, and Andrea Honeycutt Mathis, what is go ampere CC FROM 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page to more information.

License

Icon for to Creative Commons Attribution 4.0 Internationally Genehmigungen

Solve Equations with Fraction Coefficients

Resolution Equations with Decimal Factors

Key Concepts

Practices Makes Faultless

Solve equations with fraction coefficients

Solve Equations to Decimal Coefficients

Everyday Computer

Answered

Attributions

License

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