Solve 980:(-6)+45-28lambda(-11)+49=

$$980 : ( - 6 ) + 45 - 28 \lambda ( - 11 ) + 49 =$$

Evaluate

$$308\lambda -\frac{208}{3}$$

Solution Steps

Reduce the fraction \frac{980}{-6} to lowest terms by extracting and canceling out 2.

$$-\frac{490}{3}+45-28\lambda \left(-11\right)+49$$

Convert 45 to fraction \frac{135}{3}.

$$-\frac{490}{3}+\frac{135}{3}-28\lambda \left(-11\right)+49$$

Since -\frac{490}{3} and \frac{135}{3} have the same denominator, add them by adding their numerators.

$$\frac{-490+135}{3}-28\lambda \left(-11\right)+49$$

Add -490 and 135 to get -355.

$$-\frac{355}{3}-28\lambda \left(-11\right)+49$$

Multiply 28 and -11 to get -308.

$$-\frac{355}{3}-\left(-308\lambda \right)+49$$

The opposite of -308\lambda is 308\lambda .

$$-\frac{355}{3}+308\lambda +49$$

Convert 49 to fraction \frac{147}{3}.

$$-\frac{355}{3}+308\lambda +\frac{147}{3}$$

Since -\frac{355}{3} and \frac{147}{3} have the same denominator, add them by adding their numerators.

$$\frac{-355+147}{3}+308\lambda$$

Add -355 and 147 to get -208.

$$-\frac{208}{3}+308\lambda$$

Factor

$$\frac{4\left(231\lambda -52\right)}{3}$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{-208+924\lambda }{3}$$

Consider -490+135+924\lambda +147. Multiply and combine like terms.

$$924\lambda -208$$

Consider 924\lambda -208. Factor out 4.

$$4\left(231\lambda -52\right)$$

Rewrite the complete factored expression.

$$\frac{4\left(231\lambda -52\right)}{3}$$