Solve 2|1/4-3|-|3+4|

$$2 | \frac { 1 } { 4 } - 3 | - | 3 + 4 |$$

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$2|\frac{1}{4}-\frac{12}{4}|-|3+4|$$

Since \frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$2|\frac{1-12}{4}|-|3+4|$$

Subtract 12 from 1 to get -11.

$$2|-\frac{11}{4}|-|3+4|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{11}{4} is \frac{11}{4}.

$$2\times \frac{11}{4}-|3+4|$$

Express 2\times \frac{11}{4} as a single fraction.

$$\frac{2\times 11}{4}-|3+4|$$

Multiply 2 and 11 to get 22.

$$\frac{22}{4}-|3+4|$$

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$\frac{11}{2}-|3+4|$$

Add 3 and 4 to get 7.

$$\frac{11}{2}-|7|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$\frac{11}{2}-7$$

Convert 7 to fraction \frac{14}{2}.

$$\frac{11}{2}-\frac{14}{2}$$

Since \frac{11}{2} and \frac{14}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-14}{2}$$

Subtract 14 from 11 to get -3.

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

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$