Solve x-4/3-3x+1/4>-2

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

Solve for x

$$x<1$$

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.

$$4\left(x-4\right)-3\left(3x+1\right)>-24$$

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

$$4x-16-3\left(3x+1\right)>-24$$

Use the distributive property to multiply -3 by 3x+1.

$$4x-16-9x-3>-24$$

Combine 4x and -9x to get -5x.

$$-5x-16-3>-24$$

Subtract 3 from -16 to get -19.

$$-5x-19>-24$$

Add 19 to both sides.

$$-5x>-24+19$$

Add -24 and 19 to get -5.

$$-5x>-5$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x<\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x<1$$