Solve x+17/3-3x-7/4leq2

$$\frac{ x+17 }{ 3 } - \frac{ 3x-7 }{ 4 } \leq 2$$

Solve for x

$$x\geq 13$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4. Since 12 is positive, the inequality direction remains the same.

$$4\left(x+17\right)-3\left(3x-7\right)\leq 24$$

Use the distributive property to multiply 4 by x+17.

$$4x+68-3\left(3x-7\right)\leq 24$$

Use the distributive property to multiply -3 by 3x-7.

$$4x+68-9x+21\leq 24$$

Combine 4x and -9x to get -5x.

$$-5x+68+21\leq 24$$

Add 68 and 21 to get 89.

$$-5x+89\leq 24$$

Subtract 89 from both sides.

$$-5x\leq 24-89$$

Subtract 89 from 24 to get -65.

$$-5x\leq -65$$

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

$$x\geq \frac{-65}{-5}$$

Divide -65 by -5 to get 13.

$$x\geq 13$$