Question

Solve $\frac{4}{5}x+7=\frac{3}{15}x-3$

1. $-16\frac{2}{3}$
2. $-14\frac{4}{9}$
   
3. $-6\frac{2}{3}$
4. $-10$
   

Short answer

The solution of the given equation is $x=-16\frac{2}{3}$. The correct option is A.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{4}{5}x+7=\frac{3}{15}x-3$”.

Step 2. Solve the given equation.

Solving,

$\frac{4}{5}x+7=\frac{3}{15}x-3$ (Given equation)

$\frac{4}{5}x+7=\frac{1}{5}x-3$ (Simplify)

$\frac{4}{5}x+7-\frac{1}{5}x=\frac{1}{5}x-3-\frac{1}{5}x$ (Subtract $\frac{1}{5}x$from both sides)

$\frac{3}{5}x+7=-3$ (Simplify)

$\frac{3}{5}x+7-7=-3-7$ (Subtract 7 from both sides)

$\frac{3}{5}x=-10$ (Simplify)

$\frac{3}{5}x\times \frac{5}{3}=-10\times \frac{5}{3}$ (Multiply both sides by $\frac{5}{3}$)

$x=-\frac{50}{3}$ (Simplify)

$x=-16\frac{2}{3}$ (Convert to mixed fraction)

So, $x=-16\frac{2}{3}$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=-16\frac{2}{3}$in the given equation $\frac{4}{5}x+7=\frac{3}{15}x-3$to get,

$\begin{array}{l}\frac{4}{5}\left(-16\frac{2}{3}\right)+7=\frac{3}{15}\left(-16\frac{2}{3}\right)-3\\ \frac{4}{5}\left(-\frac{50}{3}\right)+7=\frac{1}{5}\left(-\frac{50}{3}\right)-3\\ 4\left(-\frac{10}{3}\right)+7=\left(-\frac{10}{3}\right)-3\\ -\frac{40}{3}+7=-\frac{10}{3}-3\end{array}$

On further simplification,

$\begin{array}{l}\frac{-40+21}{3}=\frac{-10-9}{3}\\ \frac{-19}{3}=\frac{-19}{3}\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.