Solve 3(x-6/4)leq2(x+2/3)

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

Solve for x

$$x\leq 70$$

Solution Steps

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

$$9\left(x-6\right)\leq 8\left(x+2\right)$$

Use the distributive property to multiply 9 by x-6.

$$9x-54\leq 8\left(x+2\right)$$

Use the distributive property to multiply 8 by x+2.

$$9x-54\leq 8x+16$$

Subtract 8x from both sides.

$$9x-54-8x\leq 16$$

Combine 9x and -8x to get x.

$$x-54\leq 16$$

Add 54 to both sides.

$$x\leq 16+54$$

Add 16 and 54 to get 70.

$$x\leq 70$$