Reasoning: Kiera and Javier are grouping equations based on the number of operations needed to solve them. In

order to solve the equation -4(-9 + x) = 57, Kiera

says that you need three operations. Javier says you

need two operations. Their teacher says that they are

both correct. Which operations do you need to use to

solve the equation in three operations? Use a pencil

and paper. Explain how you can use two operations to

solve the equation. Which method do you prefer?

Why?

Step-by-step explanation:

Given the -4(-9 + x) = 57, to solve this equation, follow the following steps:

Expend the parentheses at the left hand side using the distributive law.

-4(-9)+(-4x) = 57

Open the bracket by multiplying

+36-4x= 57

Subtract 36 from both sides

36-4x-36 = 57-36

-4x = 21

Divide both sides by -4

-4x/-4 = 21/-4

x = -21/4

From the calculation, we can see that we used 3 operations (multiplication, subtraction and division operations)

The most preferred is multiplication operation because the operation helps to simplify the parentheses using the distributive law in step 1.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1