Solve for q 8q-3<10q+7

$8 q - 3 < 10 q + 7$

Step 1

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

Subtract $10 q$ from both sides of the inequality.

$8 q - 3 - 10 q < 7$

Subtract $10 q$ from $8 q$ .

$- 2 q - 3 < 7$

Step 2

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

Add $3$ to both sides of the inequality.

$- 2 q < 7 + 3$

Add $7$ and $3$ .

$- 2 q < 10$

Step 3

Divide each term in $- 2 q < 10$ by $- 2$ and simplify.

Divide each term in $- 2 q < 10$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 q}{- 2} > \frac{10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 q}{- 2} > \frac{10}{- 2}$

Divide $q$ by $1$ .

$q > \frac{10}{- 2}$

Simplify the right side.

Divide $10$ by $- 2$ .

$q > - 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$q > - 5$

Interval Notation:

$(- 5, \infty)$

Solve for q 8q-3<10q+7

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