Solve 4x/9-5<3-2x/3

$$\frac { 4 x } { 9 } - 5 < 3 - \frac { 2 x } { 3 }$$

Solve for x

$$x<\frac{36}{5}$$

Solution Steps

Multiply both sides of the equation by 9, the least common multiple of 9,3. Since 9 is positive, the inequality direction remains the same.

$$4x-45<27-3\times 2x$$

Multiply -3 and 2 to get -6.

$$4x-45<27-6x$$

Add 6x to both sides.

$$4x-45+6x<27$$

Combine 4x and 6x to get 10x.

$$10x-45<27$$

Add 45 to both sides.

$$10x<27+45$$

Add 27 and 45 to get 72.

$$10x<72$$

Divide both sides by 10. Since 10 is positive, the inequality direction remains the same.

$$x<\frac{72}{10}$$

Reduce the fraction \frac{72}{10} to lowest terms by extracting and canceling out 2.

$$x<\frac{36}{5}$$