Solve 8(5x-4)-6(3x+5)leq-7

$$8 ( 5 x - 4 ) - 6 ( 3 x + 5 ) \leq - 7$$

Solve for x

$$x\leq \frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 8 by 5x-4.

$$40x-32-6\left(3x+5\right)\leq -7$$

Use the distributive property to multiply -6 by 3x+5.

$$40x-32-18x-30\leq -7$$

Combine 40x and -18x to get 22x.

$$22x-32-30\leq -7$$

Subtract 30 from -32 to get -62.

$$22x-62\leq -7$$

Add 62 to both sides.

$$22x\leq -7+62$$

Add -7 and 62 to get 55.

$$22x\leq 55$$

Divide both sides by 22. Since 22 is positive, the inequality direction remains the same.

$$x\leq \frac{55}{22}$$

Reduce the fraction \frac{55}{22} to lowest terms by extracting and canceling out 11.

$$x\leq \frac{5}{2}$$