Solve for x |2x-1|=|x+3|

$| 2 x - 1 | = | x + 3 |$

Rewrite the equation as $| x + 3 | = | 2 x - 1 |$ .

$| x + 3 | = | 2 x - 1 |$

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

$x + 3 = 2 x - 1$

$x + 3 = - (2 x - 1)$

$- (x + 3) = 2 x - 1$

$- (x + 3) = - (2 x - 1)$

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

$x + 3 = 2 x - 1$

$x + 3 = - (2 x - 1)$

Solve $x + 3 = 2 x - 1$ for $x$ .

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

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

$x + 3 - 2 x = - 1$

Subtract $2 x$ from $x$ .

$- x + 3 = - 1$

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

Subtract $3$ from both sides of the equation.

$- x = - 1 - 3$

Subtract $3$ from $- 1$ .

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$

Solve $x + 3 = - (2 x - 1)$ for $x$ .

Simplify $- (2 x - 1)$ .

Rewrite.

$x + 3 = 0 + 0 - (2 x - 1)$

Simplify by adding zeros.

$x + 3 = - (2 x - 1)$

Apply the distributive property.

$x + 3 = - (2 x) - - 1$

Multiply.

Multiply $2$ by $- 1$ .

$x + 3 = - 2 x - - 1$

Multiply $- 1$ by $- 1$ .

$x + 3 = - 2 x + 1$

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

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

$x + 3 + 2 x = 1$

Add $x$ and $2 x$ .

$3 x + 3 = 1$

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

Subtract $3$ from both sides of the equation.

$3 x = 1 - 3$

Subtract $3$ from $1$ .

$3 x = - 2$

Divide each term in $3 x = - 2$ by $3$ and simplify.

Divide each term in $3 x = - 2$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

List all of the solutions.

$x = 4, - \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = 4, - \frac{2}{3}$

Decimal Form:

$x = 4, - 0.\overline{6}$

Solve for x |2x-1|=|x+3|

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