Question

Mary began to solve the proportion x−43=2x−1 by using cross products.

She continued correctly solving the problem until she got stuck. Analyze Mary's work below.


3(2)60=(x−4)(x−1)=x2−5x+4=x2−5x−2


What step should Mary take next and why?


a. Mary should isolate the x2 term because she can then take the square root of both sides of the equation to solve for x.


b. Mary should isolate the constant because she can then factor the remaining terms and use the Zero Product Property to solve for x.


c. Mary should isolate the x term because she can then simplify the remaining expression to solve for x.


d. Mary should factor the expression to find the roots because the coefficient of the x2 term is 1 so it is easily factored.


e.Mary should use the quadratic formula to find the solutions since the expression is not factorable over the integers.

Answer 1

The answer is c :" Mary should isolate the x term because she can then simplify the remaining expression to solve for x."

Explanation:

From the equation as written below,

(x-4)(x-1)= 60

the first step is expansion of the bracket, thus we have,

x2-4x-x+4=3(2)60

which equals

x2-5x+4=3(2)60

then the next step should be to isolate x terms to be on one side of the equation while she continues solving for x,

x2-5x= 3(2)60-4

This is because in such simple equations, x could only be found if all terms of x are isolated in one side of the equation before continuing other processes such as factorization,etc.