Solve 3a/4-1-a/3leq2

$$\frac { 3 a } { 4 } - \frac { 1 - a } { 3 } \leq 2$$

Solve for a

$$a\leq \frac{28}{13}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\times 3a-4\left(1-a\right)\leq 24$$

Multiply 3 and 3 to get 9.

$$9a-4\left(1-a\right)\leq 24$$

Use the distributive property to multiply -4 by 1-a.

$$9a-4+4a\leq 24$$

Combine 9a and 4a to get 13a.

$$13a-4\leq 24$$

Add 4 to both sides.

$$13a\leq 24+4$$

Add 24 and 4 to get 28.

$$13a\leq 28$$

Divide both sides by 13. Since 13 is positive, the inequality direction remains the same.

$$a\leq \frac{28}{13}$$