Solve x/3+2leq3x+5/3-x+2/4

$$\frac{ x }{ 3 } +2 \leq \frac{ 3x+5 }{ 3 } - \frac{ x+2 }{ 4 }$$

Solve for x

$$x\geq 2$$

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.

$$4x+24\leq 4\left(3x+5\right)-3\left(x+2\right)$$

Use the distributive property to multiply 4 by 3x+5.

$$4x+24\leq 12x+20-3\left(x+2\right)$$

Use the distributive property to multiply -3 by x+2.

$$4x+24\leq 12x+20-3x-6$$

Combine 12x and -3x to get 9x.

$$4x+24\leq 9x+20-6$$

Subtract 6 from 20 to get 14.

$$4x+24\leq 9x+14$$

Subtract 9x from both sides.

$$4x+24-9x\leq 14$$

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

$$-5x+24\leq 14$$

Subtract 24 from both sides.

$$-5x\leq 14-24$$

Subtract 24 from 14 to get -10.

$$-5x\leq -10$$

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

$$x\geq \frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x\geq 2$$