Solve a/4+3ageq3a-1/2

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

Solve for a

$$a\geq -\frac{2}{7}$$

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.

$$a+12a\geq 2\left(3a-1\right)$$

Combine a and 12a to get 13a.

$$13a\geq 2\left(3a-1\right)$$

Use the distributive property to multiply 2 by 3a-1.

$$13a\geq 6a-2$$

Subtract 6a from both sides.

$$13a-6a\geq -2$$

Combine 13a and -6a to get 7a.

$$7a\geq -2$$

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

$$a\geq -\frac{2}{7}$$