Solve -2(4n-7)leq10-3(n-8)

$$- 2 ( 4 n - 7 ) \leq 10 - 3 ( n - 8 )$$

Solve for n

$$n\geq -4$$

Solution Steps

Use the distributive property to multiply -2 by 4n-7.

$$-8n+14\leq 10-3\left(n-8\right)$$

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

$$-8n+14\leq 10-3n+24$$

Add 10 and 24 to get 34.

$$-8n+14\leq 34-3n$$

Add 3n to both sides.

$$-8n+14+3n\leq 34$$

Combine -8n and 3n to get -5n.

$$-5n+14\leq 34$$

Subtract 14 from both sides.

$$-5n\leq 34-14$$

Subtract 14 from 34 to get 20.

$$-5n\leq 20$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$n\geq \frac{20}{-5}$$

Divide 20 by -5 to get -4.

$$n\geq -4$$