Solve left|0+3right|-left|0-1right|<0-3/2

$$\left| 0+3 \right| - \left| 0-1 \right| < 0- \frac{ 3 }{ 2 }$$

Verify

Solution Steps

Add 0 and 3 to get 3.

$$|3|-|0-1|<0-\frac{3}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 3 is 3.

$$3-|0-1|<0-\frac{3}{2}$$

Subtract 1 from 0 to get -1.

$$3-|-1|<0-\frac{3}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -1 is 1.

$$3-1<0-\frac{3}{2}$$

Subtract 1 from 3 to get 2.

$$2<0-\frac{3}{2}$$

Subtract \frac{3}{2} from 0 to get -\frac{3}{2}.

$$2<-\frac{3}{2}$$

Convert 2 to fraction \frac{4}{2}.

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

Compare \frac{4}{2} and -\frac{3}{2}.

$$\text{false}$$