Solve 2-a+4/3>5+2a/2

$$2 - \frac { a + 4 } { 3 } > \frac { 5 + 2 a } { 2 }$$

Solve for a

$$a<-\frac{11}{8}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$12-2\left(a+4\right)>3\left(5+2a\right)$$

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

$$12-2a-8>3\left(5+2a\right)$$

Subtract 8 from 12 to get 4.

$$4-2a>3\left(5+2a\right)$$

Use the distributive property to multiply 3 by 5+2a.

$$4-2a>15+6a$$

Subtract 6a from both sides.

$$4-2a-6a>15$$

Combine -2a and -6a to get -8a.

$$4-8a>15$$

Subtract 4 from both sides.

$$-8a>15-4$$

Subtract 4 from 15 to get 11.

$$-8a>11$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$a<-\frac{11}{8}$$