Solve x/4-1>x/3-11/2

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

Solve for x

$$x<6$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,2. Since 12 is positive, the inequality direction remains the same.

$$3x-12>4x-6\left(2+1\right)$$

Add 2 and 1 to get 3.

$$3x-12>4x-6\times 3$$

Multiply -6 and 3 to get -18.

$$3x-12>4x-18$$

Subtract 4x from both sides.

$$3x-12-4x>-18$$

Combine 3x and -4x to get -x.

$$-x-12>-18$$

Add 12 to both sides.

$$-x>-18+12$$

Add -18 and 12 to get -6.

$$-x>-6$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-6}{-1}$$

Fraction \frac{-6}{-1} can be simplified to 6 by removing the negative sign from both the numerator and the denominator.

$$x<6$$