Solve 3(3x+5)-5(2x-8)leq3(4x+1)-16

$$3 ( 3 x + 5 ) - 5 ( 2 x - 8 ) \leq 3 ( 4 x + 1 ) - 16$$

Solve for x

$$x\geq \frac{68}{13}$$

Solution Steps

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

$$9x+15-5\left(2x-8\right)\leq 3\left(4x+1\right)-16$$

Use the distributive property to multiply -5 by 2x-8.

$$9x+15-10x+40\leq 3\left(4x+1\right)-16$$

Combine 9x and -10x to get -x.

$$-x+15+40\leq 3\left(4x+1\right)-16$$

Add 15 and 40 to get 55.

$$-x+55\leq 3\left(4x+1\right)-16$$

Use the distributive property to multiply 3 by 4x+1.

$$-x+55\leq 12x+3-16$$

Subtract 16 from 3 to get -13.

$$-x+55\leq 12x-13$$

Subtract 12x from both sides.

$$-x+55-12x\leq -13$$

Combine -x and -12x to get -13x.

$$-13x+55\leq -13$$

Subtract 55 from both sides.

$$-13x\leq -13-55$$

Subtract 55 from -13 to get -68.

$$-13x\leq -68$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq \frac{-68}{-13}$$

Fraction \frac{-68}{-13} can be simplified to \frac{68}{13} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{68}{13}$$