Chapter 4.6, Problem 39WE

To determine

To find: The solution set of the equation $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ .

Answer to Problem 39WE

The solution set for the equation $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ is $\left\{\frac{20}{11}\right\}$ .

Explanation of Solution

Given information:

The equation is $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ .

Calculation:

The given equation is $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ .

Solve the given equation $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ to obtain the value of solution set.

  $\begin{array}{c}\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0\\ 2x^2-8x-5x+20+2x-2x^2=0\\ -11x+20=0\left(\text{merge the like terms}\right)\\ -11x=-20\left(\text{subtract 20 on both sides}\right)\end{array}$

Further solve the above calculation,

  $\begin{array}{c}11x=20\left(\text{multiply}-\text{on both sides}\right)\\ x=\frac{20}{11}\left(\text{divide both side by 11}\right)\text{\& }\end{array}$

Therefore, the solution set for the equation $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ is $\left\{\frac{20}{11}\right\}$ .

Conclusion:

Thus, the solution set for the equation $\left(2x-5\right)\left(x-4\right)+2x\left(1-x\right)=0$ is $\left\{\frac{20}{11}\right\}$ .