Solve the Absolute Value Inequality for r |2r+3|=|5r-17|

$| 2 r + 3 | = | 5 r - 17 |$

Rewrite the equation as $| 5 r - 17 | = | 2 r + 3 |$ .

$| 5 r - 17 | = | 2 r + 3 |$

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

$5 r - 17 = 2 r + 3$

$5 r - 17 = - (2 r + 3)$

$- (5 r - 17) = 2 r + 3$

$- (5 r - 17) = - (2 r + 3)$

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

$5 r - 17 = 2 r + 3$

$5 r - 17 = - (2 r + 3)$

Solve $5 r - 17 = 2 r + 3$ for $r$ .

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

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

$5 r - 17 - 2 r = 3$

Subtract $2 r$ from $5 r$ .

$3 r - 17 = 3$

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

Add $17$ to both sides of the equation.

$3 r = 3 + 17$

Add $3$ and $17$ .

$3 r = 20$

Divide each term in $3 r = 20$ by $3$ and simplify.

Divide each term in $3 r = 20$ by $3$ .

$\frac{3 r}{3} = \frac{20}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 r}{3} = \frac{20}{3}$

Divide $r$ by $1$ .

$r = \frac{20}{3}$

Solve $5 r - 17 = - (2 r + 3)$ for $r$ .

Simplify $- (2 r + 3)$ .

Rewrite.

$5 r - 17 = 0 + 0 - (2 r + 3)$

Simplify by adding zeros.

$5 r - 17 = - (2 r + 3)$

Apply the distributive property.

$5 r - 17 = - (2 r) - 1 \cdot 3$

Multiply.

Multiply $2$ by $- 1$ .

$5 r - 17 = - 2 r - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$5 r - 17 = - 2 r - 3$

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

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

$5 r - 17 + 2 r = - 3$

Add $5 r$ and $2 r$ .

$7 r - 17 = - 3$

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

Add $17$ to both sides of the equation.

$7 r = - 3 + 17$

Add $- 3$ and $17$ .

$7 r = 14$

Divide each term in $7 r = 14$ by $7$ and simplify.

Divide each term in $7 r = 14$ by $7$ .

$\frac{7 r}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 r}{7} = \frac{14}{7}$

Divide $r$ by $1$ .

$r = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$r = 2$

List all of the solutions.

$r = \frac{20}{3}, 2$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{20}{3}, 2$

Decimal Form:

$r = 6.\overline{6}, 2$

Mixed Number Form:

$r = 6 \frac{2}{3}, 2$

Solve the Absolute Value Inequality for r |2r+3|=|5r-17|

Related Questions

Support LCMGCF.com by disabling your adblocker.