Solve for x 4|x+2|=|2x+7|

$4 | x + 2 | = | 2 x + 7 |$

Rewrite the equation as $| 2 x + 7 | = 4 | x + 2 |$ .

$| 2 x + 7 | = 4 | x + 2 |$

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

$2 x + 7 = 4 (x + 2)$

$2 x + 7 = - 4 (x + 2)$

$- (2 x + 7) = 4 (x + 2)$

$- (2 x + 7) = - 4 (x + 2)$

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

$2 x + 7 = 4 (x + 2)$

$2 x + 7 = - 4 (x + 2)$

Solve $2 x + 7 = 4 (x + 2)$ for $x$ .

Simplify $4 (x + 2)$ .

Rewrite.

$2 x + 7 = 0 + 0 + 4 (x + 2)$

Simplify by adding zeros.

$2 x + 7 = 4 (x + 2)$

Apply the distributive property.

$2 x + 7 = 4 x + 4 \cdot 2$

Multiply $4$ by $2$ .

$2 x + 7 = 4 x + 8$

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

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

$2 x + 7 - 4 x = 8$

Subtract $4 x$ from $2 x$ .

$- 2 x + 7 = 8$

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

Subtract $7$ from both sides of the equation.

$- 2 x = 8 - 7$

Subtract $7$ from $8$ .

$- 2 x = 1$

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{1}{- 2}$

Divide $x$ by $1$ .

$x = \frac{1}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Solve $2 x + 7 = - 4 (x + 2)$ for $x$ .

Simplify $- 4 (x + 2)$ .

Rewrite.

$2 x + 7 = 0 + 0 - 4 (x + 2)$

Simplify by adding zeros.

$2 x + 7 = - 4 (x + 2)$

Apply the distributive property.

$2 x + 7 = - 4 x - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$2 x + 7 = - 4 x - 8$

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

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

$2 x + 7 + 4 x = - 8$

Add $2 x$ and $4 x$ .

$6 x + 7 = - 8$

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

Subtract $7$ from both sides of the equation.

$6 x = - 8 - 7$

Subtract $7$ from $- 8$ .

$6 x = - 15$

Divide each term in $6 x = - 15$ by $6$ and simplify.

Divide each term in $6 x = - 15$ by $6$ .

$\frac{6 x}{6} = \frac{- 15}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 15}{6}$

Divide $x$ by $1$ .

$x = \frac{- 15}{6}$

Simplify the right side.

Cancel the common factor of $- 15$ and $6$ .

Factor $3$ out of $- 15$ .

$x = \frac{3 (- 5)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot - 5}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot - 5}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{- 5}{2}$

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

List all of the solutions.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5, - 2.5$

Mixed Number Form:

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

Solve for x 4|x+2|=|2x+7|

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