Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{5}\mathbf{=}\mathbf{-}\mathbf{19}\mathbf{-}\frac{\mathbf{x}}{\mathbf{7}}$

Short answer

The solution for the equation$-5=-19-\frac{x}{7}$is $x=-98$. $x=-98$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}-5=-19-\frac{x}{7}\\ -5+19=-\frac{x}{7}\\ 14=-\frac{x}{7}\end{array}$

.  Solve for x

Now, multiply both sides of the equation by 7.

$\begin{array}{l}14\times 7=-\frac{x}{7}\times 7\\ 14\times 7=-x\\ 98=-x\\ x=-98\end{array}$

Therefore, the solution of the equation is$x=-98$.

. Check the solution 

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

$-5=-19-\frac{x}{7}$

Now, substitute $x=-98$and check the result.

$\begin{array}{l}-5=-19-\frac{\left(-98\right)}{7}\\ -5=-19+\frac{98}{7}\\ -5=-19+14\\ -5=-5\end{array}$

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

$\begin{array}{l}-5=-19-\frac{\left(-98\right)}{7}\\ -5=-19+\frac{98}{7}\\ -5=-19+14\\ -5=-5\end{array}$