Solve for y |8y+4|=2|y-1|

$| 8 y + 4 | = 2 | y - 1 |$

Step 1

Rewrite the equation as $2 | y - 1 | = | 8 y + 4 |$ .

$2 | y - 1 | = | 8 y + 4 |$

Step 2

Divide each term in $2 | y - 1 | = | 8 y + 4 |$ by $2$ and simplify.

Divide each term in $2 | y - 1 | = | 8 y + 4 |$ by $2$ .

$\frac{2 | y - 1 |}{2} = \frac{| 8 y + 4 |}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | y - 1 |}{2} = \frac{| 8 y + 4 |}{2}$

Divide $| y - 1 |$ by $1$ .

$| y - 1 | = \frac{| 8 y + 4 |}{2}$

Step 3

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

$y - 1 = \frac{8 y + 4}{2}$

$y - 1 = - \frac{8 y + 4}{2}$

$- (y - 1) = \frac{8 y + 4}{2}$

$- (y - 1) = - \frac{8 y + 4}{2}$

Step 4

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

$y - 1 = \frac{8 y + 4}{2}$

$y - 1 = - \frac{8 y + 4}{2}$

Step 5

Solve $y - 1 = \frac{8 y + 4}{2}$ for $y$ .

Cancel the common factor of $8 y + 4$ and $2$ .

Factor $2$ out of $8 y$ .

$y - 1 = \frac{2 (4 y) + 4}{2}$

Factor $2$ out of $4$ .

$y - 1 = \frac{2 (4 y) + 2 \cdot 2}{2}$

Factor $2$ out of $2 (4 y) + 2 (2)$ .

$y - 1 = \frac{2 (4 y + 2)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y - 1 = \frac{2 (4 y + 2)}{2 (1)}$

Cancel the common factor.

$y - 1 = \frac{2 (4 y + 2)}{2 \cdot 1}$

Rewrite the expression.

$y - 1 = \frac{4 y + 2}{1}$

Divide $4 y + 2$ by $1$ .

$y - 1 = 4 y + 2$

Solve for $y$ .

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

Subtract $4 y$ from both sides of the equation.

$y - 1 - 4 y = 2$

Subtract $4 y$ from $y$ .

$- 3 y - 1 = 2$

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

Add $1$ to both sides of the equation.

$- 3 y = 2 + 1$

Add $2$ and $1$ .

$- 3 y = 3$

Divide each term in $- 3 y = 3$ by $- 3$ and simplify.

Divide each term in $- 3 y = 3$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{3}{- 3}$

Divide $y$ by $1$ .

$y = \frac{3}{- 3}$

Simplify the right side.

Divide $3$ by $- 3$ .

$y = - 1$

Step 6

Solve $y - 1 = - \frac{8 y + 4}{2}$ for $y$ .

Cancel the common factor of $8 y + 4$ and $2$ .

Factor $2$ out of $8 y$ .

$y - 1 = - \frac{2 (4 y) + 4}{2}$

Factor $2$ out of $4$ .

$y - 1 = - \frac{2 (4 y) + 2 \cdot 2}{2}$

Factor $2$ out of $2 (4 y) + 2 (2)$ .

$y - 1 = - \frac{2 (4 y + 2)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y - 1 = - \frac{2 (4 y + 2)}{2 (1)}$

Cancel the common factor.

$y - 1 = - \frac{2 (4 y + 2)}{2 \cdot 1}$

Rewrite the expression.

$y - 1 = - \frac{4 y + 2}{1}$

Divide $4 y + 2$ by $1$ .

$y - 1 = - (4 y + 2)$

Solve for $y$ .

Simplify $- (4 y + 2)$ .

Rewrite.

$y - 1 = 0 + 0 - (4 y + 2)$

Simplify by adding zeros.

$y - 1 = - (4 y + 2)$

Apply the distributive property.

$y - 1 = - (4 y) - 1 \cdot 2$

Multiply.

Multiply $4$ by $- 1$ .

$y - 1 = - 4 y - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$y - 1 = - 4 y - 2$

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

Add $4 y$ to both sides of the equation.

$y - 1 + 4 y = - 2$

Add $y$ and $4 y$ .

$5 y - 1 = - 2$

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

Add $1$ to both sides of the equation.

$5 y = - 2 + 1$

Add $- 2$ and $1$ .

$5 y = - 1$

Divide each term in $5 y = - 1$ by $5$ and simplify.

Divide each term in $5 y = - 1$ by $5$ .

$\frac{5 y}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 1}{5}$

Divide $y$ by $1$ .

$y = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{1}{5}$

Step 7

List all of the solutions.

$y = - 1, - \frac{1}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$y = - 1, - \frac{1}{5}$

Decimal Form:

$y = - 1, - 0.2$

Solve for y |8y+4|=2|y-1|

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