Solve for x |4x+5|=|-29+4x|

$| 4 x + 5 | = | - 29 + 4 x |$

Rewrite the equation as $| - 29 + 4 x | = | 4 x + 5 |$ .

$| - 29 + 4 x | = | 4 x + 5 |$

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

$- 29 + 4 x = 4 x + 5$

$- 29 + 4 x = - (4 x + 5)$

$- (- 29 + 4 x) = 4 x + 5$

$- (- 29 + 4 x) = - (4 x + 5)$

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

$- 29 + 4 x = 4 x + 5$

$- 29 + 4 x = - (4 x + 5)$

Solve $- 29 + 4 x = 4 x + 5$ for $x$ .

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

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

$- 29 + 4 x - 4 x = 5$

Combine the opposite terms in $- 29 + 4 x - 4 x$ .

Subtract $4 x$ from $4 x$ .

$- 29 + 0 = 5$

Add $- 29$ and $0$ .

$- 29 = 5$

Since $- 29 \neq 5$ , there are no solutions.

No solution

Solve $- 29 + 4 x = - (4 x + 5)$ for $x$ .

Simplify $- (4 x + 5)$ .

Rewrite.

$- 29 + 4 x = 0 + 0 - (4 x + 5)$

Simplify by adding zeros.

$- 29 + 4 x = - (4 x + 5)$

Apply the distributive property.

$- 29 + 4 x = - (4 x) - 1 \cdot 5$

Multiply.

Multiply $4$ by $- 1$ .

$- 29 + 4 x = - 4 x - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$- 29 + 4 x = - 4 x - 5$

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

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

$- 29 + 4 x + 4 x = - 5$

Add $4 x$ and $4 x$ .

$- 29 + 8 x = - 5$

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

Add $29$ to both sides of the equation.

$8 x = - 5 + 29$

Add $- 5$ and $29$ .

$8 x = 24$

Divide each term in $8 x = 24$ by $8$ and simplify.

Divide each term in $8 x = 24$ by $8$ .

$\frac{8 x}{8} = \frac{24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{24}{8}$

Divide $x$ by $1$ .

$x = \frac{24}{8}$

Simplify the right side.

Divide $24$ by $8$ .

$x = 3$

Solve for x |4x+5|=|-29+4x|

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