Solve 3a-1/4geq-9/2a

$$\frac { 3 a - 1 } { 4 } \geq - \frac { 9 } { 2 } a$$

Solve for a

$$a\geq \frac{1}{21}$$

Solution Steps

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

$$3a-1\geq -18a$$

Add 18a to both sides.

$$3a-1+18a\geq 0$$

Combine 3a and 18a to get 21a.

$$21a-1\geq 0$$

Add 1 to both sides. Anything plus zero gives itself.

$$21a\geq 1$$

Divide both sides by 21. Since 21 is positive, the inequality direction remains the same.

$$a\geq \frac{1}{21}$$