Solve the Inequality for q -6q+7<=8q-3

$- 6 q + 7 \leq 8 q - 3$

Step 1

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

Subtract $8 q$ from both sides of the inequality.

$- 6 q + 7 - 8 q \leq - 3$

Subtract $8 q$ from $- 6 q$ .

$- 14 q + 7 \leq - 3$

Step 2

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

Subtract $7$ from both sides of the inequality.

$- 14 q \leq - 3 - 7$

Subtract $7$ from $- 3$ .

$- 14 q \leq - 10$

Step 3

Divide each term in $- 14 q \leq - 10$ by $- 14$ and simplify.

Divide each term in $- 14 q \leq - 10$ by $- 14$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 14 q}{- 14} \geq \frac{- 10}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 q}{- 14} \geq \frac{- 10}{- 14}$

Divide $q$ by $1$ .

$q \geq \frac{- 10}{- 14}$

Simplify the right side.

Cancel the common factor of $- 10$ and $- 14$ .

Factor $- 2$ out of $- 10$ .

$q \geq \frac{- 2 (5)}{- 14}$

Cancel the common factors.

Factor $- 2$ out of $- 14$ .

$q \geq \frac{- 2 \cdot 5}{- 2 \cdot 7}$

Cancel the common factor.

$q \geq \frac{- 2 \cdot 5}{- 2 \cdot 7}$

Rewrite the expression.

$q \geq \frac{5}{7}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$q \geq \frac{5}{7}$

Interval Notation:

$[\frac{5}{7}, \infty)$

Solve the Inequality for q -6q+7<=8q-3

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