Solve for r 4r-5<5r+7

$4 r - 5 < 5 r + 7$

Step 1

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

Subtract $5 r$ from both sides of the inequality.

$4 r - 5 - 5 r < 7$

Subtract $5 r$ from $4 r$ .

$- r - 5 < 7$

Step 2

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

Add $5$ to both sides of the inequality.

$- r < 7 + 5$

Add $7$ and $5$ .

$- r < 12$

Step 3

Divide each term in $- r < 12$ by $- 1$ and simplify.

Divide each term in $- r < 12$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- r}{- 1} > \frac{12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{r}{1} > \frac{12}{- 1}$

Divide $r$ by $1$ .

$r > \frac{12}{- 1}$

Simplify the right side.

Divide $12$ by $- 1$ .

$r > - 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$r > - 12$

Interval Notation:

$(- 12, \infty)$

Solve for r 4r-5<5r+7

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