Solve 4/6x+2/4(2x-8)<2x

$$\frac{ 4 }{ 6 } x+ \frac{ 2 }{ 4 } (2x-8) < 2x$$

Solve for x

$$x>-12$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x+\frac{2}{4}\left(2x-8\right)<2x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x+\frac{1}{2}\left(2x-8\right)<2x$$

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

$$\frac{2}{3}x+\frac{1}{2}\times 2x+\frac{1}{2}\left(-8\right)<2x$$

Cancel out 2 and 2.

$$\frac{2}{3}x+x+\frac{1}{2}\left(-8\right)<2x$$

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

$$\frac{2}{3}x+x+\frac{-8}{2}<2x$$

Divide -8 by 2 to get -4.

$$\frac{2}{3}x+x-4<2x$$

Combine \frac{2}{3}x and x to get \frac{5}{3}x.

$$\frac{5}{3}x-4<2x$$

Subtract 2x from both sides.

$$\frac{5}{3}x-4-2x<0$$

Combine \frac{5}{3}x and -2x to get -\frac{1}{3}x.

$$-\frac{1}{3}x-4<0$$

Add 4 to both sides. Anything plus zero gives itself.

$$-\frac{1}{3}x<4$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}. Since -\frac{1}{3} is negative, the inequality direction is changed.

$$x>4\left(-3\right)$$

Multiply 4 and -3 to get -12.

$$x>-12$$