Solve 2a+3<2a-3+8-4a

$$2 a + 3 < 2 a - 3 + 8 - 4 a$$

Solve for a

$$a<\frac{1}{2}$$

Solution Steps

Add -3 and 8 to get 5.

$$2a+3<2a+5-4a$$

Combine 2a and -4a to get -2a.

$$2a+3<-2a+5$$

Add 2a to both sides.

$$2a+3+2a<5$$

Combine 2a and 2a to get 4a.

$$4a+3<5$$

Subtract 3 from both sides.

$$4a<5-3$$

Subtract 3 from 5 to get 2.

$$4a<2$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$a<\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$a<\frac{1}{2}$$