Solve 2x(-11/6-11/2)

$$2 x ( - 1 \frac { 1 } { 6 } - 1 \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{16x}{3}$$

Solution Steps

Multiply 1 and 6 to get 6.

$$2x\left(-\frac{6+1}{6}-\frac{1\times 2+1}{2}\right)$$

Add 6 and 1 to get 7.

$$2x\left(-\frac{7}{6}-\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$2x\left(-\frac{7}{6}-\frac{3}{2}\right)$$

Least common multiple of 6 and 2 is 6. Convert -\frac{7}{6} and \frac{3}{2} to fractions with denominator 6.

$$2x\left(-\frac{7}{6}-\frac{9}{6}\right)$$

Since -\frac{7}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$2x\times \frac{-7-9}{6}$$

Subtract 9 from -7 to get -16.

$$2x\times \frac{-16}{6}$$

Reduce the fraction \frac{-16}{6} to lowest terms by extracting and canceling out 2.

$$2x\left(-\frac{8}{3}\right)$$

Express 2\left(-\frac{8}{3}\right) as a single fraction.

$$\frac{2\left(-8\right)}{3}x$$

Multiply 2 and -8 to get -16.

$$\frac{-16}{3}x$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{16}{3}x$$

Expand

$$-\frac{16x}{3}$$

Solution Steps

Multiply 1 and 6 to get 6.

$$2x\left(-\frac{6+1}{6}-\frac{1\times 2+1}{2}\right)$$

Add 6 and 1 to get 7.

$$2x\left(-\frac{7}{6}-\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$2x\left(-\frac{7}{6}-\frac{3}{2}\right)$$

Least common multiple of 6 and 2 is 6. Convert -\frac{7}{6} and \frac{3}{2} to fractions with denominator 6.

$$2x\left(-\frac{7}{6}-\frac{9}{6}\right)$$

Since -\frac{7}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$2x\times \frac{-7-9}{6}$$

Subtract 9 from -7 to get -16.

$$2x\times \frac{-16}{6}$$

Reduce the fraction \frac{-16}{6} to lowest terms by extracting and canceling out 2.

$$2x\left(-\frac{8}{3}\right)$$

Express 2\left(-\frac{8}{3}\right) as a single fraction.

$$\frac{2\left(-8\right)}{3}x$$

Multiply 2 and -8 to get -16.

$$\frac{-16}{3}x$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{16}{3}x$$