Question

Solve each equation. Check your solution.

$\mathbf{2}\mathbf{x}\mathbf{-}\mathbf{7}\mathbf{-}\left(x-5\right)\mathbf{=}\mathbf{0}$

Short answer

The solution of the given equation is $\mathbf{2}$.

Step-by-step solution

– Description of step.

Expand the parentheses on the left-hand side of the given equation.

$2x-7-x+5=0$

– Description of step.

Add 7 on both the sides of the equation in step 1.

$\begin{array}{c}2x-7-x+5+7=0+7\\ 2x-x+5=7\end{array}$

– Description of step.

Subtract 5 from both the sides of the equation in step 2.

$\begin{array}{c}2x-x+5-5=7-5\\ x=2\end{array}$

– Description of step.

To check whether the obtained value of x is the solution of given equation, substitute 2 for x into $2x-7-\left(x-5\right)=0$and simplify.

$\begin{array}{d}2\cdot 2-7-\left(2-5\right)=0\\ 4-7-2+5\stackrel{?}{=}0\\ 4-9+5\stackrel{?}{=}0\\ 9-9\stackrel{?}{=}0\\ 0=0\end{array}$

Therefore, the solution of the given equation is 2.