Solve 37-2x/3+xleq3x-8/4-9

$$\frac{ 37-2x }{ 3 } +x \leq \frac{ 3x-8 }{ 4 } -9$$

Solve for x

$$x\geq 56$$

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.

$$4\left(37-2x\right)+12x\leq 3\left(3x-8\right)-108$$

Use the distributive property to multiply 4 by 37-2x.

$$148-8x+12x\leq 3\left(3x-8\right)-108$$

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

$$148+4x\leq 3\left(3x-8\right)-108$$

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

$$148+4x\leq 9x-24-108$$

Subtract 108 from -24 to get -132.

$$148+4x\leq 9x-132$$

Subtract 9x from both sides.

$$148+4x-9x\leq -132$$

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

$$148-5x\leq -132$$

Subtract 148 from both sides.

$$-5x\leq -132-148$$

Subtract 148 from -132 to get -280.

$$-5x\leq -280$$

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

$$x\geq \frac{-280}{-5}$$

Divide -280 by -5 to get 56.

$$x\geq 56$$