Solve (-11/2x+3)-2(-11/4x-5/2)=

$$( - \frac { 11 } { 2 } x + 3 ) - 2 ( - \frac { 11 } { 4 } x - \frac { 5 } { 2 } ) =$$

Evaluate

$$8$$

Solution Steps

Use the distributive property to multiply -2 by -\frac{11}{4}x-\frac{5}{2}.

$$-\frac{11}{2}x+3-2\left(-\frac{11}{4}\right)x-2\left(-\frac{5}{2}\right)$$

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

$$-\frac{11}{2}x+3+\frac{-2\left(-11\right)}{4}x-2\left(-\frac{5}{2}\right)$$

Multiply -2 and -11 to get 22.

$$-\frac{11}{2}x+3+\frac{22}{4}x-2\left(-\frac{5}{2}\right)$$

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

$$-\frac{11}{2}x+3+\frac{11}{2}x-2\left(-\frac{5}{2}\right)$$

Multiply -2 times -\frac{5}{2}.

$$-\frac{11}{2}x+3+\frac{11}{2}x+5$$

Combine -\frac{11}{2}x and \frac{11}{2}x to get 0.

$$3+5$$

Add 3 and 5 to get 8.

$$8$$

Factor

$$2^{3}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-11x+6-\left(-11x-10\right)}{2}$$

Simplify.

$$8$$