Solve the Inequality for q q+12-2(q-22)>0

$q + 12 - 2 (q - 22) > 0$

Step 1

Simplify $q + 12 - 2 (q - 22)$ .

Simplify each term.

Apply the distributive property.

$q + 12 - 2 q - 2 \cdot - 22 > 0$

Multiply $- 2$ by $- 22$ .

$q + 12 - 2 q + 44 > 0$

Simplify by adding terms.

Subtract $2 q$ from $q$ .

$- q + 12 + 44 > 0$

Add $12$ and $44$ .

$- q + 56 > 0$

Step 2

Subtract $56$ from both sides of the inequality.

$- q > - 56$

Step 3

Divide each term in $- q > - 56$ by $- 1$ and simplify.

Divide each term in $- q > - 56$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- q}{- 1} < \frac{- 56}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{q}{1} < \frac{- 56}{- 1}$

Divide $q$ by $1$ .

$q < \frac{- 56}{- 1}$

Simplify the right side.

Divide $- 56$ by $- 1$ .

$q < 56$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$q < 56$

Interval Notation:

$(- \infty, 56)$

Solve the Inequality for q q+12-2(q-22)>0

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