Solve for x |2x+5|=|-2x+1|

$| 2 x + 5 | = | - 2 x + 1 |$

Step 1

Rewrite the equation as $| - 2 x + 1 | = | 2 x + 5 |$ .

$| - 2 x + 1 | = | 2 x + 5 |$

Step 2

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

$- 2 x + 1 = 2 x + 5$

$- 2 x + 1 = - (2 x + 5)$

$- (- 2 x + 1) = 2 x + 5$

$- (- 2 x + 1) = - (2 x + 5)$

Step 3

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

$- 2 x + 1 = 2 x + 5$

$- 2 x + 1 = - (2 x + 5)$

Step 4

Solve $- 2 x + 1 = 2 x + 5$ for $x$ .

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

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

$- 2 x + 1 - 2 x = 5$

Subtract $2 x$ from $- 2 x$ .

$- 4 x + 1 = 5$

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

Subtract $1$ from both sides of the equation.

$- 4 x = 5 - 1$

Subtract $1$ from $5$ .

$- 4 x = 4$

Divide each term in $- 4 x = 4$ by $- 4$ and simplify.

Divide each term in $- 4 x = 4$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

Divide $x$ by $1$ .

$x = \frac{4}{- 4}$

Simplify the right side.

Divide $4$ by $- 4$ .

$x = - 1$

Step 5

Solve $- 2 x + 1 = - (2 x + 5)$ for $x$ .

Simplify $- (2 x + 5)$ .

Rewrite.

$- 2 x + 1 = 0 + 0 - (2 x + 5)$

Simplify by adding zeros.

$- 2 x + 1 = - (2 x + 5)$

Apply the distributive property.

$- 2 x + 1 = - (2 x) - 1 \cdot 5$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x + 1 = - 2 x - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$- 2 x + 1 = - 2 x - 5$

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

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

$- 2 x + 1 + 2 x = - 5$

Combine the opposite terms in $- 2 x + 1 + 2 x$ .

Add $- 2 x$ and $2 x$ .

$0 + 1 = - 5$

Add $0$ and $1$ .

$1 = - 5$

Since $1 \neq - 5$ , there are no solutions.

No solution

Step 6

List all of the solutions.

$x = - 1$

Solve for x |2x+5|=|-2x+1|

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