Solve the Inequality for r r+4-2(r-14)>0

$r + 4 - 2 (r - 14) > 0$

Simplify $r + 4 - 2 (r - 14)$ .

Simplify each term.

Apply the distributive property.

$r + 4 - 2 r - 2 \cdot - 14 > 0$

Multiply $- 2$ by $- 14$ .

$r + 4 - 2 r + 28 > 0$

Simplify by adding terms.

Subtract $2 r$ from $r$ .

$- r + 4 + 28 > 0$

Add $4$ and $28$ .

$- r + 32 > 0$

Subtract $32$ from both sides of the inequality.

$- r > - 32$

Divide each term in $- r > - 32$ by $- 1$ and simplify.

Divide each term in $- r > - 32$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- r}{- 1} < \frac{- 32}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{r}{1} < \frac{- 32}{- 1}$

Divide $r$ by $1$ .

$r < \frac{- 32}{- 1}$

Simplify the right side.

Divide $- 32$ by $- 1$ .

$r < 32$

The result can be shown in multiple forms.

Inequality Form:

$r < 32$

Interval Notation:

$(- \infty, 32)$

Solve the Inequality for r r+4-2(r-14)>0

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