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Q. 107

Expert-verified
Found in: Page 229

### Elementary Algebra

Book edition 2nd
Author(s) Lynn Marecek, MaryAnne Anthony-Smith
Pages 1240 pages
ISBN 9780998625713

# In the following exercise, solve each equation using the Division and Multiplication Properties of Equality and check the solution. $-\frac{7}{10}x=-\frac{14}{3}$

On solving, we get $x=\frac{20}{3}.$

See the step by step solution

## Step 1. Given information

$\begin{array}{l}\text{The given equation is}-\frac{7}{10}x=-\frac{14}{3}.\\ \text{We have to solve the given equation and then verify the result.}\end{array}$

## Step 2. Simplify

$\begin{array}{l}\text{Now,}\\ ⇒-\frac{7}{10}x=-\frac{14}{3}\\ ⇒-\frac{10}{7}×\left(-\frac{7}{10}x\right)=-\frac{10}{7}×\left(-\frac{14}{3}\right)\text{}\left[\text{Multiply both sides by reciprocal of}-\frac{7}{10}\right]\\ ⇒x=\frac{20}{3}\end{array}$

## Step 3. Checking the result

$\begin{array}{l}\text{We have,}\\ ⇒-\frac{7}{10}x=-\frac{14}{3}\\ ⇒-\frac{7}{10}\left(\frac{20}{3}\right)=-\frac{14}{3}\text{}\left[\text{Substitute}x=\frac{20}{3}\right]\\ ⇒-\frac{7}{\overline{)10}}×\frac{2×\overline{)10}}{3}=-\frac{14}{3}\\ ⇒-\frac{14}{3}=-\frac{14}{3}\\ \text{L.H.S}=\text{R.H.S}\\ \text{Hence verified.}\end{array}$