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Q35.

Expert-verified
Found in: Page 133

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Solve the equation. Check your solution.$\mathbf{13}\mathbf{y}\mathbf{+}\mathbf{19}\mathbf{=}\mathbf{54}\mathbf{+}\mathbf{6}\mathbf{y}\mathbf{+}\mathbf{14}$

The solution for the equation $13y+19=54+6y+14$ is $y=7$.

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}13y+19=54+6y+14\\ 13y+19-19=+6y+68-19\text{}\left(\text{Subtract 19 from both sides}\right)\\ 13y+0=6y+49\text{}\left(\text{Simplify}\right)\\ 13y-6y=6y-6y+49\text{}\left(\text{Subtract 6y from both sides}\right)\\ 7y=49\text{}\left(\text{Simplify}\right)\end{array}$

## Step 2 – Solve for y

Now, divide both sides of the equation by 7.

$\begin{array}{c}\frac{7y}{7}=\frac{49}{7}\\ y=7\end{array}$

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

## Step 3 – Check the solution

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

$13y+19=54+6y+14$

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

$\begin{array}{c}13×7+19=54+6×7+14\\ 91+19=54+42+14\\ 110=110\end{array}$

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