Solve for y |y-3|=2y-10

$| y - 3 | = 2 y - 10$

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

$y - 3 = \pm (2 y - 10)$

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.

$y - 3 = 2 y - 10$

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

Subtract $2 y$ from both sides of the equation.

$y - 3 - 2 y = - 10$

Subtract $2 y$ from $y$ .

$- y - 3 = - 10$

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

Add $3$ to both sides of the equation.

$- y = - 10 + 3$

Add $- 10$ and $3$ .

$- y = - 7$

Divide each term in $- y = - 7$ by $- 1$ and simplify.

Divide each term in $- y = - 7$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 7}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$y = 7$

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

$y - 3 = - (2 y - 10)$

Simplify $- (2 y - 10)$ .

Rewrite.

$y - 3 = 0 + 0 - (2 y - 10)$

Simplify by adding zeros.

$y - 3 = - (2 y - 10)$

Apply the distributive property.

$y - 3 = - (2 y) - - 10$

Multiply.

Multiply $2$ by $- 1$ .

$y - 3 = - 2 y - - 10$

Multiply $- 1$ by $- 10$ .

$y - 3 = - 2 y + 10$

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

Add $2 y$ to both sides of the equation.

$y - 3 + 2 y = 10$

Add $y$ and $2 y$ .

$3 y - 3 = 10$

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

Add $3$ to both sides of the equation.

$3 y = 10 + 3$

Add $10$ and $3$ .

$3 y = 13$

Divide each term in $3 y = 13$ by $3$ and simplify.

Divide each term in $3 y = 13$ by $3$ .

$\frac{3 y}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{13}{3}$

Divide $y$ by $1$ .

$y = \frac{13}{3}$

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

$y = 7, \frac{13}{3}$

Exclude the solutions that do not make $| y - 3 | = 2 y - 10$ true.

$y = 7$

Solve for y |y-3|=2y-10

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