Solve the Inequality for r 5r-6>8r-18

$5 r - 6 > 8 r - 18$

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

Subtract $8 r$ from both sides of the inequality.

$5 r - 6 - 8 r > - 18$

Subtract $8 r$ from $5 r$ .

$- 3 r - 6 > - 18$

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

Add $6$ to both sides of the inequality.

$- 3 r > - 18 + 6$

Add $- 18$ and $6$ .

$- 3 r > - 12$

Divide each term in $- 3 r > - 12$ by $- 3$ and simplify.

Divide each term in $- 3 r > - 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 r}{- 3} < \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 r}{- 3} < \frac{- 12}{- 3}$

Divide $r$ by $1$ .

$r < \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$r < 4$

The result can be shown in multiple forms.

Inequality Form:

$r < 4$

Interval Notation:

$(- \infty, 4)$

Solve the Inequality for r 5r-6>8r-18

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