Solve 2x(-11/4-11/2)

$$2 x ( - 1 \frac { 1 } { 4 } - 1 \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{11x}{2}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$2x\left(-\frac{4+1}{4}-\frac{1\times 2+1}{2}\right)$$

Add 4 and 1 to get 5.

$$2x\left(-\frac{5}{4}-\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 2 to get 2.

$$2x\left(-\frac{5}{4}-\frac{2+1}{2}\right)$$

Add 2 and 1 to get 3.

$$2x\left(-\frac{5}{4}-\frac{3}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$2x\left(-\frac{5}{4}-\frac{6}{4}\right)$$

Since -\frac{5}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$2x\times \frac{-5-6}{4}$$

Subtract 6 from -5 to get -11.

$$2x\left(-\frac{11}{4}\right)$$

Express 2\left(-\frac{11}{4}\right) as a single fraction.

$$\frac{2\left(-11\right)}{4}x$$

Multiply 2 and -11 to get -22.

$$\frac{-22}{4}x$$

Reduce the fraction \frac{-22}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{2}x$$

Expand

$$-\frac{11x}{2}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$2x\left(-\frac{4+1}{4}-\frac{1\times 2+1}{2}\right)$$

Add 4 and 1 to get 5.

$$2x\left(-\frac{5}{4}-\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 2 to get 2.

$$2x\left(-\frac{5}{4}-\frac{2+1}{2}\right)$$

Add 2 and 1 to get 3.

$$2x\left(-\frac{5}{4}-\frac{3}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$2x\left(-\frac{5}{4}-\frac{6}{4}\right)$$

Since -\frac{5}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$2x\times \frac{-5-6}{4}$$

Subtract 6 from -5 to get -11.

$$2x\left(-\frac{11}{4}\right)$$

Express 2\left(-\frac{11}{4}\right) as a single fraction.

$$\frac{2\left(-11\right)}{4}x$$

Multiply 2 and -11 to get -22.

$$\frac{-22}{4}x$$

Reduce the fraction \frac{-22}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{2}x$$