Solve (7/10)-7/4=3(-7/10)-2(-frac{17/10)}{5}

$$( \frac { 7 } { 10 } ) - \frac { 7 } { 4 } = 3 ( - \frac { 7 } { 10 } ) - \frac { 2 ( - \frac { 17 } { 10 } ) } { 5 }$$

Verify

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 10,4,5.

$$14-35=60\left(-\frac{7}{10}\right)-4\times 2\left(-\frac{17}{10}\right)$$

Subtract 35 from 14 to get -21.

$$-21=60\left(-\frac{7}{10}\right)-4\times 2\left(-\frac{17}{10}\right)$$

Express 60\left(-\frac{7}{10}\right) as a single fraction.

$$-21=\frac{60\left(-7\right)}{10}-4\times 2\left(-\frac{17}{10}\right)$$

Multiply 60 and -7 to get -420.

$$-21=\frac{-420}{10}-4\times 2\left(-\frac{17}{10}\right)$$

Divide -420 by 10 to get -42.

$$-21=-42-4\times 2\left(-\frac{17}{10}\right)$$

Multiply -4 and 2 to get -8.

$$-21=-42-8\left(-\frac{17}{10}\right)$$

Express -8\left(-\frac{17}{10}\right) as a single fraction.

$$-21=-42+\frac{-8\left(-17\right)}{10}$$

Multiply -8 and -17 to get 136.

$$-21=-42+\frac{136}{10}$$

Reduce the fraction \frac{136}{10} to lowest terms by extracting and canceling out 2.

$$-21=-42+\frac{68}{5}$$

Convert -42 to fraction -\frac{210}{5}.

$$-21=-\frac{210}{5}+\frac{68}{5}$$

Since -\frac{210}{5} and \frac{68}{5} have the same denominator, add them by adding their numerators.

$$-21=\frac{-210+68}{5}$$

Add -210 and 68 to get -142.

$$-21=-\frac{142}{5}$$

Convert -21 to fraction -\frac{105}{5}.

$$-\frac{105}{5}=-\frac{142}{5}$$

Compare -\frac{105}{5} and -\frac{142}{5}.

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