Solve 3(-1/12)-1/3=2(-1/12)+1/2-1

$$3 ( - \frac { 1 } { 12 } ) - \frac { 1 } { 3 } = \frac { 2 ( - \frac { 1 } { 12 } ) + 1 } { 2 } - 1$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 12,3,2.

$$36\left(-\frac{1}{12}\right)-4=6\left(2\left(-\frac{1}{12}\right)+1\right)-12$$

Express 36\left(-\frac{1}{12}\right) as a single fraction.

$$\frac{36\left(-1\right)}{12}-4=6\left(2\left(-\frac{1}{12}\right)+1\right)-12$$

Multiply 36 and -1 to get -36.

$$\frac{-36}{12}-4=6\left(2\left(-\frac{1}{12}\right)+1\right)-12$$

Divide -36 by 12 to get -3.

$$-3-4=6\left(2\left(-\frac{1}{12}\right)+1\right)-12$$

Subtract 4 from -3 to get -7.

$$-7=6\left(2\left(-\frac{1}{12}\right)+1\right)-12$$

Express 2\left(-\frac{1}{12}\right) as a single fraction.

$$-7=6\left(\frac{2\left(-1\right)}{12}+1\right)-12$$

Multiply 2 and -1 to get -2.

$$-7=6\left(\frac{-2}{12}+1\right)-12$$

Reduce the fraction \frac{-2}{12} to lowest terms by extracting and canceling out 2.

$$-7=6\left(-\frac{1}{6}+1\right)-12$$

Convert 1 to fraction \frac{6}{6}.

$$-7=6\left(-\frac{1}{6}+\frac{6}{6}\right)-12$$

Since -\frac{1}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$-7=6\times \frac{-1+6}{6}-12$$

Add -1 and 6 to get 5.

$$-7=6\times \frac{5}{6}-12$$

Cancel out 6 and 6.

$$-7=5-12$$

Subtract 12 from 5 to get -7.

$$-7=-7$$

Compare -7 and -7.

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