Solve left|5/2-4right|=4-5/2

$$\left| \frac{ 5 }{ 2 } -4 \right| =4- \frac{ 5 }{ 2 }$$

Verify

Solution Steps

Convert 4 to fraction \frac{8}{2}.

$$|\frac{5}{2}-\frac{8}{2}|=4-\frac{5}{2}$$

Since \frac{5}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{5-8}{2}|=4-\frac{5}{2}$$

Subtract 8 from 5 to get -3.

$$|-\frac{3}{2}|=4-\frac{5}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{2} is \frac{3}{2}.

$$\frac{3}{2}=4-\frac{5}{2}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{3}{2}=\frac{8}{2}-\frac{5}{2}$$

Since \frac{8}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}=\frac{8-5}{2}$$

Subtract 5 from 8 to get 3.

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

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

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