Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{24}\mathbf{s}\mathbf{-}\mathbf{53}\mathbf{=}\mathbf{39}\mathbf{-}\mathbf{s}$

Short answer

The solution for the equation $-24s-53=39-s$ is $s=-4$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-24s-53=39-s\\ -24s+s-53=39-s+s\left(\text{Add}s\text{tobothsides}\right)\\ -23s-53=39\left(\text{Simplify}\right)\\ -23s-53+53=39+53\left(\text{Add53tobothsides}\right)\\ -23s=92\left(\text{Simplify}\right)\end{array}$

– Solve for s

Now, divide both sides of the equation by -23.

$\begin{array}{c}\frac{-23s}{-23}=\frac{92}{-23}\\ s=-4\end{array}$

Therefore, the solution of the equation is $s=-4$.

– Check the solution 

To check the solution, write the original equation and substitute the value of s.

$-24s-53=39-s$

Now, substitute $s=-4$ and check the result.

$\begin{array}{c}-24\left(-4\right)-53=39-\left(-4\right)\\ 96-53=39+4\\ 43=43\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.