Solve for r 5|2r+3|-5=0

$5 | 2 r + 3 | - 5 = 0$

Step 1

Add $5$ to both sides of the equation.

$5 | 2 r + 3 | = 5$

Step 2

Divide each term in $5 | 2 r + 3 | = 5$ by $5$ and simplify.

Divide each term in $5 | 2 r + 3 | = 5$ by $5$ .

$\frac{5 | 2 r + 3 |}{5} = \frac{5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 | 2 r + 3 |}{5} = \frac{5}{5}$

Divide $| 2 r + 3 |$ by $1$ .

$| 2 r + 3 | = \frac{5}{5}$

Simplify the right side.

Divide $5$ by $5$ .

$| 2 r + 3 | = 1$

Step 3

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 r + 3 = \pm 1$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$2 r + 3 = 1$

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

Subtract $3$ from both sides of the equation.

$2 r = 1 - 3$

Subtract $3$ from $1$ .

$2 r = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $2$ .

$r = - 1$

Next, use the negative value of the $\pm$ to find the second solution.

$2 r + 3 = - 1$

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

Subtract $3$ from both sides of the equation.

$2 r = - 1 - 3$

Subtract $3$ from $- 1$ .

$2 r = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $r$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $2$ .

$r = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$r = - 1, - 2$

Solve for r 5|2r+3|-5=0

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