Solve for y |5y+3|=|5y+7|

$| 5 y + 3 | = | 5 y + 7 |$

Step 1

Rewrite the equation as $| 5 y + 7 | = | 5 y + 3 |$ .

$| 5 y + 7 | = | 5 y + 3 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$5 y + 7 = 5 y + 3$

$5 y + 7 = - (5 y + 3)$

$- (5 y + 7) = 5 y + 3$

$- (5 y + 7) = - (5 y + 3)$

Step 3

After simplifying, there are only two unique equations to be solved.

$5 y + 7 = 5 y + 3$

$5 y + 7 = - (5 y + 3)$

Step 4

Solve $5 y + 7 = 5 y + 3$ for $y$ .

Move all terms containing $y$ to the left side of the equation.

Subtract $5 y$ from both sides of the equation.

$5 y + 7 - 5 y = 3$

Combine the opposite terms in $5 y + 7 - 5 y$ .

Subtract $5 y$ from $5 y$ .

$0 + 7 = 3$

Add $0$ and $7$ .

$7 = 3$

Since $7 \neq 3$ , there are no solutions.

No solution

Step 5

Solve $5 y + 7 = - (5 y + 3)$ for $y$ .

Simplify $- (5 y + 3)$ .

Rewrite.

$5 y + 7 = 0 + 0 - (5 y + 3)$

Simplify by adding zeros.

$5 y + 7 = - (5 y + 3)$

Apply the distributive property.

$5 y + 7 = - (5 y) - 1 \cdot 3$

Multiply.

Multiply $5$ by $- 1$ .

$5 y + 7 = - 5 y - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$5 y + 7 = - 5 y - 3$

Move all terms containing $y$ to the left side of the equation.

Add $5 y$ to both sides of the equation.

$5 y + 7 + 5 y = - 3$

Add $5 y$ and $5 y$ .

$10 y + 7 = - 3$

Move all terms not containing $y$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$10 y = - 3 - 7$

Subtract $7$ from $- 3$ .

$10 y = - 10$

Divide each term in $10 y = - 10$ by $10$ and simplify.

Divide each term in $10 y = - 10$ by $10$ .

$\frac{10 y}{10} = \frac{- 10}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 10}{10}$

Divide $y$ by $1$ .

$y = \frac{- 10}{10}$

Simplify the right side.

Divide $- 10$ by $10$ .

$y = - 1$

Solve for y |5y+3|=|5y+7|

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