Solve 9-8(2n+3)leq1-6n

$$9 - 8 ( 2 n + 3 ) \leq 1 - 6 n$$

Solve for n

$$n\geq -\frac{8}{5}$$

Solution Steps

Use the distributive property to multiply -8 by 2n+3.

$$9-16n-24\leq 1-6n$$

Subtract 24 from 9 to get -15.

$$-15-16n\leq 1-6n$$

Add 6n to both sides.

$$-15-16n+6n\leq 1$$

Combine -16n and 6n to get -10n.

$$-15-10n\leq 1$$

Add 15 to both sides.

$$-10n\leq 1+15$$

Add 1 and 15 to get 16.

$$-10n\leq 16$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$n\geq \frac{16}{-10}$$

Reduce the fraction \frac{16}{-10} to lowest terms by extracting and canceling out 2.

$$n\geq -\frac{8}{5}$$