Solve for y |(2y-6)/5|=3

$| \frac{2 y - 6}{5} | = 3$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{2 y - 6}{5} = \pm 3$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$\frac{2 y - 6}{5} = 3$

Multiply both sides by $5$ .

$\frac{2 y - 6}{5} \cdot 5 = 3 \cdot 5$

Simplify.

Simplify the left side.

Simplify $\frac{2 y - 6}{5} \cdot 5$ .

Factor $2$ out of $2 y - 6$ .

Factor $2$ out of $2 y$ .

$\frac{2 (y) - 6}{5} \cdot 5 = 3 \cdot 5$

Factor $2$ out of $- 6$ .

$\frac{2 y + 2 \cdot - 3}{5} \cdot 5 = 3 \cdot 5$

Factor $2$ out of $2 y + 2 \cdot - 3$ .

$\frac{2 (y - 3)}{5} \cdot 5 = 3 \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (y - 3)}{5} \cdot 5 = 3 \cdot 5$

Rewrite the expression.

$2 (y - 3) = 3 \cdot 5$

Apply the distributive property.

$2 y + 2 \cdot - 3 = 3 \cdot 5$

Multiply $2$ by $- 3$ .

$2 y - 6 = 3 \cdot 5$

Simplify the right side.

Multiply $3$ by $5$ .

$2 y - 6 = 15$

Solve for $y$ .

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

Add $6$ to both sides of the equation.

$2 y = 15 + 6$

Add $15$ and $6$ .

$2 y = 21$

Divide each term in $2 y = 21$ by $2$ and simplify.

Divide each term in $2 y = 21$ by $2$ .

$\frac{2 y}{2} = \frac{21}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{21}{2}$

Divide $y$ by $1$ .

$y = \frac{21}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$\frac{2 y - 6}{5} = - 3$

Multiply both sides by $5$ .

$\frac{2 y - 6}{5} \cdot 5 = - 3 \cdot 5$

Simplify.

Simplify the left side.

Simplify $\frac{2 y - 6}{5} \cdot 5$ .

Factor $2$ out of $2 y - 6$ .

Factor $2$ out of $2 y$ .

$\frac{2 (y) - 6}{5} \cdot 5 = - 3 \cdot 5$

Factor $2$ out of $- 6$ .

$\frac{2 y + 2 \cdot - 3}{5} \cdot 5 = - 3 \cdot 5$

Factor $2$ out of $2 y + 2 \cdot - 3$ .

$\frac{2 (y - 3)}{5} \cdot 5 = - 3 \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (y - 3)}{5} \cdot 5 = - 3 \cdot 5$

Rewrite the expression.

$2 (y - 3) = - 3 \cdot 5$

Apply the distributive property.

$2 y + 2 \cdot - 3 = - 3 \cdot 5$

Multiply $2$ by $- 3$ .

$2 y - 6 = - 3 \cdot 5$

Simplify the right side.

Multiply $- 3$ by $5$ .

$2 y - 6 = - 15$

Solve for $y$ .

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

Add $6$ to both sides of the equation.

$2 y = - 15 + 6$

Add $- 15$ and $6$ .

$2 y = - 9$

Divide each term in $2 y = - 9$ by $2$ and simplify.

Divide each term in $2 y = - 9$ by $2$ .

$\frac{2 y}{2} = \frac{- 9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 9}{2}$

Divide $y$ by $1$ .

$y = \frac{- 9}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{9}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{21}{2}, - \frac{9}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{21}{2}, - \frac{9}{2}$

Decimal Form:

$y = 10.5, - 4.5$

Mixed Number Form:

$y = 10 \frac{1}{2}, - 4 \frac{1}{2}$

Solve for y |(2y-6)/5|=3

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