Question

Solve each equation. Check your solution.

$\frac{2}{5}x+6=\frac{2}{3}x+10$

Short answer

The solution of the given equation is $x=-15$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{2}{5}x+6=\frac{2}{3}x+10$”.

Step 2. Solve the given equation.

Solving,

$\frac{2}{5}x+6=\frac{2}{3}x+10$ (Given equation)

$\frac{2}{5}x+6-\frac{2}{3}x=\frac{2}{3}x+10-\frac{2}{3}x$ (Subtract $\frac{2}{3}x$from both sides)

$-\frac{4}{15}x+6=10$ (Simplify)

$-\frac{4}{15}x+6-6=10-6$ (Subtract 6 from both sides)

$-\frac{4}{15}x=4$

$-\frac{4}{15}x\times \left(-\frac{15}{4}\right)=4\times \left(-\frac{15}{4}\right)$ (Multiply both sides by $-\frac{15}{4}$)

$x=-15$ (Simplify)

So, $x=-15$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=-15$in the given equation $\frac{2}{5}x+6=\frac{2}{3}x+10$to get,

$\begin{array}{l}\frac{2}{5}\left(-15\right)+6=\frac{2}{3}\left(-15\right)+10\\ 2\left(-3\right)+6=2\left(-5\right)+10\\ -6+6=-10+10\\ 0=0\end{array}$

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.