Solve for x |4x+6|=2x+27

$| 4 x + 6 | = 2 x + 27$

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

$4 x + 6 = \pm (2 x + 27)$

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.

$4 x + 6 = 2 x + 27$

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

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

$4 x + 6 - 2 x = 27$

Subtract $2 x$ from $4 x$ .

$2 x + 6 = 27$

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

Subtract $6$ from both sides of the equation.

$2 x = 27 - 6$

Subtract $6$ from $27$ .

$2 x = 21$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

$4 x + 6 = - (2 x + 27)$

Simplify $- (2 x + 27)$ .

Rewrite.

$4 x + 6 = 0 + 0 - (2 x + 27)$

Simplify by adding zeros.

$4 x + 6 = - (2 x + 27)$

Apply the distributive property.

$4 x + 6 = - (2 x) - 1 \cdot 27$

Multiply.

Multiply $2$ by $- 1$ .

$4 x + 6 = - 2 x - 1 \cdot 27$

Multiply $- 1$ by $27$ .

$4 x + 6 = - 2 x - 27$

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

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

$4 x + 6 + 2 x = - 27$

Add $4 x$ and $2 x$ .

$6 x + 6 = - 27$

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

Subtract $6$ from both sides of the equation.

$6 x = - 27 - 6$

Subtract $6$ from $- 27$ .

$6 x = - 33$

Divide each term in $6 x = - 33$ by $6$ and simplify.

Divide each term in $6 x = - 33$ by $6$ .

$\frac{6 x}{6} = \frac{- 33}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 33}{6}$

Divide $x$ by $1$ .

$x = \frac{- 33}{6}$

Simplify the right side.

Cancel the common factor of $- 33$ and $6$ .

Factor $3$ out of $- 33$ .

$x = \frac{3 (- 11)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 11}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot - 11}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{- 11}{2}$

Move the negative in front of the fraction.

$x = - \frac{11}{2}$

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

$x = \frac{21}{2}, - \frac{11}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21}{2}, - \frac{11}{2}$

Decimal Form:

$x = 10.5, - 5.5$

Mixed Number Form:

$x = 10 \frac{1}{2}, - 5 \frac{1}{2}$

Solve for x |4x+6|=2x+27

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