Solve left|-5/4-2right|=3(-5/4)-7

$$\left| - \frac{ 5 }{ 4 } -2 \right| = 3(- \frac{ 5 }{ 4 } )-7$$

Verify

Solution Steps

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

$$|-\frac{5}{4}-\frac{8}{4}|=3\left(-\frac{5}{4}\right)-7$$

Since -\frac{5}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{-5-8}{4}|=3\left(-\frac{5}{4}\right)-7$$

Subtract 8 from -5 to get -13.

$$|-\frac{13}{4}|=3\left(-\frac{5}{4}\right)-7$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{13}{4} is \frac{13}{4}.

$$\frac{13}{4}=3\left(-\frac{5}{4}\right)-7$$

Express 3\left(-\frac{5}{4}\right) as a single fraction.

$$\frac{13}{4}=\frac{3\left(-5\right)}{4}-7$$

Multiply 3 and -5 to get -15.

$$\frac{13}{4}=\frac{-15}{4}-7$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{13}{4}=-\frac{15}{4}-7$$

Convert 7 to fraction \frac{28}{4}.

$$\frac{13}{4}=-\frac{15}{4}-\frac{28}{4}$$

Since -\frac{15}{4} and \frac{28}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{4}=\frac{-15-28}{4}$$

Subtract 28 from -15 to get -43.

$$\frac{13}{4}=-\frac{43}{4}$$

Compare \frac{13}{4} and -\frac{43}{4}.

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