Solve 4x-8/2leq2/3x+6

$$\frac { 4 x - 8 } { 2 } \leq \frac { 2 } { 3 } x + 6$$

Solve for x

$$x\leq \frac{15}{2}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\left(4x-8\right)\leq 4x+36$$

Use the distributive property to multiply 3 by 4x-8.

$$12x-24\leq 4x+36$$

Subtract 4x from both sides.

$$12x-24-4x\leq 36$$

Combine 12x and -4x to get 8x.

$$8x-24\leq 36$$

Add 24 to both sides.

$$8x\leq 36+24$$

Add 36 and 24 to get 60.

$$8x\leq 60$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x\leq \frac{60}{8}$$

Reduce the fraction \frac{60}{8} to lowest terms by extracting and canceling out 4.

$$x\leq \frac{15}{2}$$