Solve for q 4q+5>=6q-7

$4 q + 5 \geq 6 q - 7$

Step 1

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

Subtract $6 q$ from both sides of the inequality.

$4 q + 5 - 6 q \geq - 7$

Subtract $6 q$ from $4 q$ .

$- 2 q + 5 \geq - 7$

Step 2

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

Subtract $5$ from both sides of the inequality.

$- 2 q \geq - 7 - 5$

Subtract $5$ from $- 7$ .

$- 2 q \geq - 12$

Step 3

Divide each term in $- 2 q \geq - 12$ by $- 2$ and simplify.

Divide each term in $- 2 q \geq - 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 q}{- 2} \leq \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 q}{- 2} \leq \frac{- 12}{- 2}$

Divide $q$ by $1$ .

$q \leq \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$q \leq 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$q \leq 6$

Interval Notation:

$(- \infty, 6]$

Solve for q 4q+5>=6q-7

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