Solve 2x/3-3x/4geq2

$$\frac{ 2x }{ 3 } - \frac{ 3x }{ 4 } \geq 2$$

Solve for x

$$x\leq -24$$

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.

$$4\times 2x-3\times 3x\geq 24$$

Multiply 4 and 2 to get 8.

$$8x-3\times 3x\geq 24$$

Multiply -3 and 3 to get -9.

$$8x-9x\geq 24$$

Combine 8x and -9x to get -x.

$$-x\geq 24$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq -24$$