Solve 2x/3-x-1/2>2/9

$$\frac { 2 x } { 3 } - \frac { x - 1 } { 2 } > \frac { 2 } { 9 }$$

Solve for x

$$x>-\frac{5}{3}$$

Solution Steps

Multiply both sides of the equation by 18, the least common multiple of 3,2,9. Since 18 is positive, the inequality direction remains the same.

$$6\times 2x-9\left(x-1\right)>4$$

Multiply 6 and 2 to get 12.

$$12x-9\left(x-1\right)>4$$

Use the distributive property to multiply -9 by x-1.

$$12x-9x+9>4$$

Combine 12x and -9x to get 3x.

$$3x+9>4$$

Subtract 9 from both sides.

$$3x>4-9$$

Subtract 9 from 4 to get -5.

$$3x>-5$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x>-\frac{5}{3}$$