Q55. - Algebra 1

Question

Solve each equation. Check your solution. 

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

Step-by-Step Solution

Answer

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

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.