Solve 2/3a-2/3<1/2a

$$\frac { 2 } { 3 } a - \frac { 2 } { 3 } < \frac { 1 } { 2 } a$$

Solve for a

$$a<4$$

Solution Steps

Subtract \frac{1}{2}a from both sides.

$$\frac{2}{3}a-\frac{2}{3}-\frac{1}{2}a<0$$

Combine \frac{2}{3}a and -\frac{1}{2}a to get \frac{1}{6}a.

$$\frac{1}{6}a-\frac{2}{3}<0$$

Add \frac{2}{3} to both sides. Anything plus zero gives itself.

$$\frac{1}{6}a<\frac{2}{3}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}. Since \frac{1}{6} is positive, the inequality direction remains the same.

$$a<\frac{2}{3}\times 6$$

Express \frac{2}{3}\times 6 as a single fraction.

$$a<\frac{2\times 6}{3}$$

Multiply 2 and 6 to get 12.

$$a<\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$a<4$$