Solve a-2/3<2+3a/4

$$\frac { a - 2 } { 3 } < 2 + \frac { 3 a } { 4 }$$

Solve for a

$$a>-\frac{32}{5}$$

Solution Steps

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

$$4\left(a-2\right)<24+3\times 3a$$

Use the distributive property to multiply 4 by a-2.

$$4a-8<24+3\times 3a$$

Multiply 3 and 3 to get 9.

$$4a-8<24+9a$$

Subtract 9a from both sides.

$$4a-8-9a<24$$

Combine 4a and -9a to get -5a.

$$-5a-8<24$$

Add 8 to both sides.

$$-5a<24+8$$

Add 24 and 8 to get 32.

$$-5a<32$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$a>-\frac{32}{5}$$