Question

Your friend solved the equation in the box shown. What should your friend do to correct the error that he made$?$

$\begin{array}{rcl}-\frac{x}{3}+\frac{2}{5}& =& -\frac{7}{15}\\ -\frac{x}{3}+\frac{2}{5}-\frac{2}{5}& =& -\frac{7}{15}-\frac{2}{5}\\ -\frac{x}{3}& =& -\frac{13}{15}\\ 3\bullet \left(-\frac{x}{3}\right)& =& 3\bullet \left(-\frac{13}{15}\right)\\ x& =& -2\frac{3}{5}\\ & & \end{array}$

• A. Add $\frac{2}{5}$ to each side to get $-\frac{x}{3}=-\frac{1}{15}$
• B. Multiply each side $-3$ to get $x+\frac{2}{5}=\frac{7}{5}$
• C. Multiply each side $-3$ to get $x=2\frac{3}{5}$
• D. Subtract $\frac{2}{5}$ from each side to get $-\frac{x}{3}=-\frac{5}{10}$.

Answer 1

The correct option is C

Multiply each side $-3$ to get $x=2\frac{3}{5}$

Find the incorrect part in solved equation.

Given, equation is

$\Rightarrow -\frac{x}{3}+\frac{2}{5}=-\frac{7}{15}$

We can solve the given equation as:

$$\begin{gathered} \Rightarrow -\frac{x}{3}+\frac{2}{5}=-\frac{7}{15} \\ \Rightarrow -\frac{x}{3}+\frac{2}{5}-\frac{2}{5}=-\frac{7}{15}-\frac{2}{5} \\ \Rightarrow -\frac{x}{3}=-\frac{13}{15} \\ \Rightarrow -3\times (-\frac{x}{3})=-3\times (-\frac{13}{15})..........\left(1\right) \\ \Rightarrow x=2\frac{3}{5} \end{gathered}$$

So, from equation $\left(1\right)$ in above solution, it is clear that both side is multiplied by $-3$ after which the result is $2\frac{3}{5}$.

Hence, the correct answer is option (C).