Solve =6-71/2-1+3-lambda/1-lambda=8

$$= \frac { 6 - 71 } { 2 - 1 } + \frac { 3 - \lambda } { 1 - \lambda } = 8$$

Solve for λ

$$\lambda =\frac{35}{36}\approx 0.972222222$$

Steps for Solving Linear Equation

Variable \lambda cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by -\lambda +1.

$$\left(-\lambda +1\right)\left(6-71\right)+3-\lambda =8\left(-\lambda +1\right)$$

Subtract 71 from 6 to get -65.

$$\left(-\lambda +1\right)\left(-65\right)+3-\lambda =8\left(-\lambda +1\right)$$

Use the distributive property to multiply -\lambda +1 by -65.

$$65\lambda -65+3-\lambda =8\left(-\lambda +1\right)$$

Add -65 and 3 to get -62.

$$65\lambda -62-\lambda =8\left(-\lambda +1\right)$$

Combine 65\lambda and -\lambda to get 64\lambda .

$$64\lambda -62=8\left(-\lambda +1\right)$$

Use the distributive property to multiply 8 by -\lambda +1.

$$64\lambda -62=-8\lambda +8$$

Add 8\lambda to both sides.

$$64\lambda -62+8\lambda =8$$

Combine 64\lambda and 8\lambda to get 72\lambda .

$$72\lambda -62=8$$

Add 62 to both sides.

$$72\lambda =8+62$$

Add 8 and 62 to get 70.

$$72\lambda =70$$

Divide both sides by 72.

$$\lambda =\frac{70}{72}$$

Reduce the fraction \frac{70}{72} to lowest terms by extracting and canceling out 2.

$$\lambda =\frac{35}{36}$$