Solve 8(1/2x-1/4)>12-2x

$$8 ( \frac { 1 } { 2 } x - \frac { 1 } { 4 } ) > 12 - 2 x$$

Solve for x

$$x>\frac{7}{3}$$

Solution Steps

Use the distributive property to multiply 8 by \frac{1}{2}x-\frac{1}{4}.

$$8\times \frac{1}{2}x+8\left(-\frac{1}{4}\right)>12-2x$$

Multiply 8 and \frac{1}{2} to get \frac{8}{2}.

$$\frac{8}{2}x+8\left(-\frac{1}{4}\right)>12-2x$$

Divide 8 by 2 to get 4.

$$4x+8\left(-\frac{1}{4}\right)>12-2x$$

Express 8\left(-\frac{1}{4}\right) as a single fraction.

$$4x+\frac{8\left(-1\right)}{4}>12-2x$$

Multiply 8 and -1 to get -8.

$$4x+\frac{-8}{4}>12-2x$$

Divide -8 by 4 to get -2.

$$4x-2>12-2x$$

Add 2x to both sides.

$$4x-2+2x>12$$

Combine 4x and 2x to get 6x.

$$6x-2>12$$

Add 2 to both sides.

$$6x>12+2$$

Add 12 and 2 to get 14.

$$6x>14$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x>\frac{14}{6}$$

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$x>\frac{7}{3}$$