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

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

Verify

Solution Steps

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

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

Express 2\left(-\frac{7}{10}\right) as a single fraction.

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

Multiply 2 and -7 to get -14.

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

Reduce the fraction \frac{-14}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{5}-35=60\left(-\frac{7}{10}\right)-4\times 2\times \frac{-17}{10}$$

Convert 35 to fraction \frac{175}{5}.

$$-\frac{7}{5}-\frac{175}{5}=60\left(-\frac{7}{10}\right)-4\times 2\times \frac{-17}{10}$$

Since -\frac{7}{5} and \frac{175}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-175}{5}=60\left(-\frac{7}{10}\right)-4\times 2\times \frac{-17}{10}$$

Subtract 175 from -7 to get -182.

$$-\frac{182}{5}=60\left(-\frac{7}{10}\right)-4\times 2\times \frac{-17}{10}$$

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

$$-\frac{182}{5}=\frac{60\left(-7\right)}{10}-4\times 2\times \frac{-17}{10}$$

Multiply 60 and -7 to get -420.

$$-\frac{182}{5}=\frac{-420}{10}-4\times 2\times \frac{-17}{10}$$

Divide -420 by 10 to get -42.

$$-\frac{182}{5}=-42-4\times 2\times \frac{-17}{10}$$

Multiply -4 and 2 to get -8.

$$-\frac{182}{5}=-42-8\times \frac{-17}{10}$$

Fraction \frac{-17}{10} can be rewritten as -\frac{17}{10} by extracting the negative sign.

$$-\frac{182}{5}=-42-8\left(-\frac{17}{10}\right)$$

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

$$-\frac{182}{5}=-42+\frac{-8\left(-17\right)}{10}$$

Multiply -8 and -17 to get 136.

$$-\frac{182}{5}=-42+\frac{136}{10}$$

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

$$-\frac{182}{5}=-42+\frac{68}{5}$$

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

$$-\frac{182}{5}=-\frac{210}{5}+\frac{68}{5}$$

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

$$-\frac{182}{5}=\frac{-210+68}{5}$$

Add -210 and 68 to get -142.

$$-\frac{182}{5}=-\frac{142}{5}$$

Compare -\frac{182}{5} and -\frac{142}{5}.

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