Solve 1/3x-1/4(x+2)>3x-11/3

$$\frac { 1 } { 3 } x - \frac { 1 } { 4 } ( x + 2 ) > 3 x - 1 \frac { 1 } { 3 }$$

Solve for x

$$x<\frac{2}{7}$$

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.

$$4x-3\left(x+2\right)>36x-4\left(3+1\right)$$

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

$$4x-3x-6>36x-4\left(3+1\right)$$

Combine 4x and -3x to get x.

$$x-6>36x-4\left(3+1\right)$$

Add 3 and 1 to get 4.

$$x-6>36x-4\times 4$$

Multiply -4 and 4 to get -16.

$$x-6>36x-16$$

Subtract 36x from both sides.

$$x-6-36x>-16$$

Combine x and -36x to get -35x.

$$-35x-6>-16$$

Add 6 to both sides.

$$-35x>-16+6$$

Add -16 and 6 to get -10.

$$-35x>-10$$

Divide both sides by -35. Since -35 is negative, the inequality direction is changed.

$$x<\frac{-10}{-35}$$

Reduce the fraction \frac{-10}{-35} to lowest terms by extracting and canceling out -5.

$$x<\frac{2}{7}$$