Solve -1/6x-2x-5/4geq3-8x-3/3

$$- \frac { 1 } { 6 } x - \frac { 2 x - 5 } { 4 } \geq 3 - \frac { 8 x - 3 } { 3 }$$

Solve for x

$$x\geq \frac{11}{8}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 6,4,3. Since 12 is positive, the inequality direction remains the same.

$$-2x-3\left(2x-5\right)\geq 36-4\left(8x-3\right)$$

Use the distributive property to multiply -3 by 2x-5.

$$-2x-6x+15\geq 36-4\left(8x-3\right)$$

Combine -2x and -6x to get -8x.

$$-8x+15\geq 36-4\left(8x-3\right)$$

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

$$-8x+15\geq 36-32x+12$$

Add 36 and 12 to get 48.

$$-8x+15\geq 48-32x$$

Add 32x to both sides.

$$-8x+15+32x\geq 48$$

Combine -8x and 32x to get 24x.

$$24x+15\geq 48$$

Subtract 15 from both sides.

$$24x\geq 48-15$$

Subtract 15 from 48 to get 33.

$$24x\geq 33$$

Divide both sides by 24. Since 24 is positive, the inequality direction remains the same.

$$x\geq \frac{33}{24}$$

Reduce the fraction \frac{33}{24} to lowest terms by extracting and canceling out 3.

$$x\geq \frac{11}{8}$$