Solve 3x-2/12-0x-3/24-2x-1/6geq-12/8

$$\frac { 3 x - 2 } { 12 } - \frac { 0 x - 3 } { 24 } - \frac { 2 x - 1 } { 6 } \geq - 1 \frac { 2 } { 8 }$$

Solve for x

$$x\leq \frac{33}{2}$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 12,24,6,8. Since 24 is positive, the inequality direction remains the same.

$$2\left(3x-2\right)-\left(0x-3\right)-4\left(2x-1\right)\geq -3\left(8+2\right)$$

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

$$6x-4-\left(0x-3\right)-4\left(2x-1\right)\geq -3\left(8+2\right)$$

Anything times zero gives zero.

$$6x-4-\left(0-3\right)-4\left(2x-1\right)\geq -3\left(8+2\right)$$

Subtract 3 from 0 to get -3.

$$6x-4-\left(-3\right)-4\left(2x-1\right)\geq -3\left(8+2\right)$$

The opposite of -3 is 3.

$$6x-4+3-4\left(2x-1\right)\geq -3\left(8+2\right)$$

Add -4 and 3 to get -1.

$$6x-1-4\left(2x-1\right)\geq -3\left(8+2\right)$$

Use the distributive property to multiply -4 by 2x-1.

$$6x-1-8x+4\geq -3\left(8+2\right)$$

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

$$-2x-1+4\geq -3\left(8+2\right)$$

Add -1 and 4 to get 3.

$$-2x+3\geq -3\left(8+2\right)$$

Add 8 and 2 to get 10.

$$-2x+3\geq -3\times 10$$

Multiply -3 and 10 to get -30.

$$-2x+3\geq -30$$

Subtract 3 from both sides.

$$-2x\geq -30-3$$

Subtract 3 from -30 to get -33.

$$-2x\geq -33$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\leq \frac{-33}{-2}$$

Fraction \frac{-33}{-2} can be simplified to \frac{33}{2} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{33}{2}$$