Question

Solve the equation. Check your solution.

$\mathbf{8}\mathbf{y}\mathbf{+}\mathbf{4}\mathbf{=}\mathbf{11}\mathbf{y}\mathbf{-}\mathbf{17}$

Short answer

The solution for the equation $\text{8}y+4=11y-17$is$y=7$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}\text{8}y+4=11y-17\\ 8y+4-8y=11y-17-8y\text{[Substract8}y\text{fromeachside.]}\\ 4=3y-17\text{[Simplify.]}\\ 4+17=3y-17+17\text{[Add17oneachside.]}\\ 21=3y\text{[Simplify.]}\end{array}$

– Solve for y

Now, divide both sides of the equation by 3.

$\begin{array}{c}\frac{21}{3}=\frac{3y}{3}\\ y=7\end{array}$

Therefore, the solution of the equation is $y=7$.

– Check the solution 

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

$\text{8}y+4=11y-17$

Now, substitute $y=7$and check the result.

$\begin{array}{c}\text{8(7)}+\text{4}=\text{11(7)}-17\\ 56+4=77-17\\ \text{60}=\text{60}\end{array}$

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