Solve for r |r+2|=|3r-4|

$| r + 2 | = | 3 r - 4 |$

Rewrite the equation as $| 3 r - 4 | = | r + 2 |$ .

$| 3 r - 4 | = | r + 2 |$

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

$3 r - 4 = r + 2$

$3 r - 4 = - (r + 2)$

$- (3 r - 4) = r + 2$

$- (3 r - 4) = - (r + 2)$

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

$3 r - 4 = r + 2$

$3 r - 4 = - (r + 2)$

Solve $3 r - 4 = r + 2$ for $r$ .

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

Subtract $r$ from both sides of the equation.

$3 r - 4 - r = 2$

Subtract $r$ from $3 r$ .

$2 r - 4 = 2$

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

Add $4$ to both sides of the equation.

$2 r = 2 + 4$

Add $2$ and $4$ .

$2 r = 6$

Divide each term in $2 r = 6$ by $2$ and simplify.

Divide each term in $2 r = 6$ by $2$ .

$\frac{2 r}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 r}{2} = \frac{6}{2}$

Divide $r$ by $1$ .

$r = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$r = 3$

Solve $3 r - 4 = - (r + 2)$ for $r$ .

Simplify $- (r + 2)$ .

Rewrite.

$3 r - 4 = 0 + 0 - (r + 2)$

Simplify by adding zeros.

$3 r - 4 = - (r + 2)$

Apply the distributive property.

$3 r - 4 = - r - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$3 r - 4 = - r - 2$

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

Add $r$ to both sides of the equation.

$3 r - 4 + r = - 2$

Add $3 r$ and $r$ .

$4 r - 4 = - 2$

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

Add $4$ to both sides of the equation.

$4 r = - 2 + 4$

Add $- 2$ and $4$ .

$4 r = 2$

Divide each term in $4 r = 2$ by $4$ and simplify.

Divide each term in $4 r = 2$ by $4$ .

$\frac{4 r}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r}{4} = \frac{2}{4}$

Divide $r$ by $1$ .

$r = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$r = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$r = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$r = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$r = \frac{1}{2}$

List all of the solutions.

$r = 3, \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$r = 3, \frac{1}{2}$

Decimal Form:

$r = 3, 0.5$

Solve for r |r+2|=|3r-4|

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