Question

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

Answer 1

Answer:

d. Mary should factor the expression to find the roots because the coefficient of $x^{2}$ term is 1 so it is easily factored.

Step-by-step explanation:

$x^{2}$ - 5x + 4 = 0

Factoring the above equation gives

(x - 4)(x - 1) = 0

Now, if either of the terms (x - 4) or (x - 1) is 0, the product is zero, so we can conclude that

(x - 4) = 0, therefore

x = 4

or

(x - 1) = 0, therefore

x = 1

Hence the the roots are x = 4 and x = 1

we  can check the root in the original equation by substitution to see if we are correct

when x =4

$x^{2}$ - 5x + 4

$(4)^{2}$ - 5(4) + 4 = 16 - 20 + 4 = 0

when x = 1

$x^{2}$ - 5x + 4

$(1)^{2}$ - 5(1) + 4 = 1 - 5 + 4 = 0

Answer 2

Answer:

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

Step-by-step 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.