Solve the Absolute Value Inequality for r 3|3-5r|-3=18

$3 | 3 - 5 r | - 3 = 18$

Move all terms not containing $| 3 - 5 r |$ to the right side of the equation.

Add $3$ to both sides of the equation.

$3 | 3 - 5 r | = 18 + 3$

Add $18$ and $3$ .

$3 | 3 - 5 r | = 21$

Divide each term in $3 | 3 - 5 r | = 21$ by $3$ and simplify.

Divide each term in $3 | 3 - 5 r | = 21$ by $3$ .

$\frac{3 | 3 - 5 r |}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | 3 - 5 r |}{3} = \frac{21}{3}$

Divide $| 3 - 5 r |$ by $1$ .

$| 3 - 5 r | = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$| 3 - 5 r | = 7$

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

$3 - 5 r = \pm 7$

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.

$3 - 5 r = 7$

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

Subtract $3$ from both sides of the equation.

$- 5 r = 7 - 3$

Subtract $3$ from $7$ .

$- 5 r = 4$

Divide each term in $- 5 r = 4$ by $- 5$ and simplify.

Divide each term in $- 5 r = 4$ by $- 5$ .

$\frac{- 5 r}{- 5} = \frac{4}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 r}{- 5} = \frac{4}{- 5}$

Divide $r$ by $1$ .

$r = \frac{4}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$r = - \frac{4}{5}$

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

$3 - 5 r = - 7$

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

Subtract $3$ from both sides of the equation.

$- 5 r = - 7 - 3$

Subtract $3$ from $- 7$ .

$- 5 r = - 10$

Divide each term in $- 5 r = - 10$ by $- 5$ and simplify.

Divide each term in $- 5 r = - 10$ by $- 5$ .

$\frac{- 5 r}{- 5} = \frac{- 10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 r}{- 5} = \frac{- 10}{- 5}$

Divide $r$ by $1$ .

$r = \frac{- 10}{- 5}$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$r = 2$

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

$r = - \frac{4}{5}, 2$

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{4}{5}, 2$

Decimal Form:

$r = - 0.8, 2$

Solve the Absolute Value Inequality for r 3|3-5r|-3=18

Related Questions

Support LCMGCF.com by disabling your adblocker.