Solve lambda/2+2+4(lambda/4+1)-3

$$\frac { \lambda } { 2 } + 2 + 4 ( \frac { \lambda } { 4 } + 1 ) - 3$$

Evaluate

$$\frac{3\left(\lambda +2\right)}{2}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\frac{\lambda }{2}+2+4\left(\frac{\lambda }{4}+\frac{4}{4}\right)-3$$

Since \frac{\lambda }{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{\lambda }{2}+2+4\times \frac{\lambda +4}{4}-3$$

Cancel out 4 and 4.

$$\frac{\lambda }{2}+2+\lambda +4-3$$

Combine \frac{\lambda }{2} and \lambda to get \frac{3}{2}\lambda .

$$\frac{3}{2}\lambda +2+4-3$$

Add 2 and 4 to get 6.

$$\frac{3}{2}\lambda +6-3$$

Subtract 3 from 6 to get 3.

$$\frac{3}{2}\lambda +3$$

Expand

$$\frac{3\lambda }{2}+3$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\frac{\lambda }{2}+2+4\left(\frac{\lambda }{4}+\frac{4}{4}\right)-3$$

Since \frac{\lambda }{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{\lambda }{2}+2+4\times \frac{\lambda +4}{4}-3$$

Cancel out 4 and 4.

$$\frac{\lambda }{2}+2+\lambda +4-3$$

Combine \frac{\lambda }{2} and \lambda to get \frac{3}{2}\lambda .

$$\frac{3}{2}\lambda +2+4-3$$

Add 2 and 4 to get 6.

$$\frac{3}{2}\lambda +6-3$$

Subtract 3 from 6 to get 3.

$$\frac{3}{2}\lambda +3$$