Solve 8(-61/10)-1/6=3(-61/10)+10

$$\frac { 8 ( - \frac { 61 } { 10 } ) - 1 } { 6 } = 3 ( - \frac { 61 } { 10 } ) + 10$$

Verify

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 6,10.

$$5\left(8\left(-\frac{61}{10}\right)-1\right)=90\left(-\frac{61}{10}\right)+300$$

Express 8\left(-\frac{61}{10}\right) as a single fraction.

$$5\left(\frac{8\left(-61\right)}{10}-1\right)=90\left(-\frac{61}{10}\right)+300$$

Multiply 8 and -61 to get -488.

$$5\left(\frac{-488}{10}-1\right)=90\left(-\frac{61}{10}\right)+300$$

Reduce the fraction \frac{-488}{10} to lowest terms by extracting and canceling out 2.

$$5\left(-\frac{244}{5}-1\right)=90\left(-\frac{61}{10}\right)+300$$

Convert 1 to fraction \frac{5}{5}.

$$5\left(-\frac{244}{5}-\frac{5}{5}\right)=90\left(-\frac{61}{10}\right)+300$$

Since -\frac{244}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$5\times \frac{-244-5}{5}=90\left(-\frac{61}{10}\right)+300$$

Subtract 5 from -244 to get -249.

$$5\left(-\frac{249}{5}\right)=90\left(-\frac{61}{10}\right)+300$$

Cancel out 5 and 5.

$$-249=90\left(-\frac{61}{10}\right)+300$$

Express 90\left(-\frac{61}{10}\right) as a single fraction.

$$-249=\frac{90\left(-61\right)}{10}+300$$

Multiply 90 and -61 to get -5490.

$$-249=\frac{-5490}{10}+300$$

Divide -5490 by 10 to get -549.

$$-249=-549+300$$

Add -549 and 300 to get -249.

$$-249=-249$$

Compare -249 and -249.

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