Solve for x |4x+4|-10=3x

$| 4 x + 4 | - 10 = 3 x$

Add $10$ to both sides of the equation.

$| 4 x + 4 | = 3 x + 10$

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

$4 x + 4 = \pm (3 x + 10)$

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.

$4 x + 4 = 3 x + 10$

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

Subtract $3 x$ from both sides of the equation.

$4 x + 4 - 3 x = 10$

Subtract $3 x$ from $4 x$ .

$x + 4 = 10$

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

Subtract $4$ from both sides of the equation.

$x = 10 - 4$

Subtract $4$ from $10$ .

$x = 6$

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

$4 x + 4 = - (3 x + 10)$

Simplify $- (3 x + 10)$ .

Rewrite.

$4 x + 4 = 0 + 0 - (3 x + 10)$

Simplify by adding zeros.

$4 x + 4 = - (3 x + 10)$

Apply the distributive property.

$4 x + 4 = - (3 x) - 1 \cdot 10$

Multiply.

Multiply $3$ by $- 1$ .

$4 x + 4 = - 3 x - 1 \cdot 10$

Multiply $- 1$ by $10$ .

$4 x + 4 = - 3 x - 10$

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

Add $3 x$ to both sides of the equation.

$4 x + 4 + 3 x = - 10$

Add $4 x$ and $3 x$ .

$7 x + 4 = - 10$

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

Subtract $4$ from both sides of the equation.

$7 x = - 10 - 4$

Subtract $4$ from $- 10$ .

$7 x = - 14$

Divide each term in $7 x = - 14$ by $7$ and simplify.

Divide each term in $7 x = - 14$ by $7$ .

$\frac{7 x}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 14}{7}$

Divide $x$ by $1$ .

$x = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$x = - 2$

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

$x = 6, - 2$

Solve for x |4x+4|-10=3x

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