Solve -2(3-4*8n)leq9(4-n)

$$- 2 ( 3 - 4 \cdot 8 n ) \leq 9 ( 4 - n )$$

Solve for n

$$n\leq \frac{42}{73}$$

Solution Steps

Multiply 4 and 8 to get 32.

$$-2\left(3-32n\right)\leq 9\left(4-n\right)$$

Use the distributive property to multiply -2 by 3-32n.

$$-6+64n\leq 9\left(4-n\right)$$

Use the distributive property to multiply 9 by 4-n.

$$-6+64n\leq 36-9n$$

Add 9n to both sides.

$$-6+64n+9n\leq 36$$

Combine 64n and 9n to get 73n.

$$-6+73n\leq 36$$

Add 6 to both sides.

$$73n\leq 36+6$$

Add 36 and 6 to get 42.

$$73n\leq 42$$

Divide both sides by 73. Since 73 is positive, the inequality direction remains the same.

$$n\leq \frac{42}{73}$$