Solve for q 22q+73>52q+63

$22 q + 73 > 52 q + 63$

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

Subtract $52 q$ from both sides of the inequality.

$22 q + 73 - 52 q > 63$

Subtract $52 q$ from $22 q$ .

$- 30 q + 73 > 63$

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

Subtract $73$ from both sides of the inequality.

$- 30 q > 63 - 73$

Subtract $73$ from $63$ .

$- 30 q > - 10$

Divide each term in $- 30 q > - 10$ by $- 30$ and simplify.

Divide each term in $- 30 q > - 10$ by $- 30$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 30 q}{- 30} < \frac{- 10}{- 30}$

Simplify the left side.

Cancel the common factor of $- 30$ .

Cancel the common factor.

$\frac{- 30 q}{- 30} < \frac{- 10}{- 30}$

Divide $q$ by $1$ .

$q < \frac{- 10}{- 30}$

Simplify the right side.

Cancel the common factor of $- 10$ and $- 30$ .

Factor $- 10$ out of $- 10$ .

$q < \frac{- 10 (1)}{- 30}$

Cancel the common factors.

Factor $- 10$ out of $- 30$ .

$q < \frac{- 10 \cdot 1}{- 10 \cdot 3}$

Cancel the common factor.

$q < \frac{- 10 \cdot 1}{- 10 \cdot 3}$

Rewrite the expression.

$q < \frac{1}{3}$

The result can be shown in multiple forms.

Inequality Form:

$q < \frac{1}{3}$

Interval Notation:

$(- \infty, \frac{1}{3})$

Solve for q 22q+73>52q+63

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