Solve m/4-4<3/4-m/3

$$\frac { m } { 4 } - 4 < \frac { 3 } { 4 } - \frac { m } { 3 }$$

Solve for m

$$m<\frac{57}{7}$$

Solution Steps

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

$$3m-48<9-4m$$

Add 4m to both sides.

$$3m-48+4m<9$$

Combine 3m and 4m to get 7m.

$$7m-48<9$$

Add 48 to both sides.

$$7m<9+48$$

Add 9 and 48 to get 57.

$$7m<57$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$m<\frac{57}{7}$$