Question

Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles. Which explains why Bernard added 5 negative x-tiles to both sides in the first step of the solution?
A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side.

B) He wanted to combine more negative tiles with the 4 negative tiles on the left side of the equation.

C) He wanted to remove the larger coefficient on the left side of the equation.

D) He wanted to have 10 x-tiles on the left side of the equation.

Answer 1

A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side

Answer 2

To find why he would do this, we need to understand what all the possible first steps are in this equation.

You could add 4 to both sides.
You could subtract 4 from both sides.
You could subtract 5x from both sides.
You could subtract 6x from both sides.

Any of these work. In Bernard's case, he added 5 negative x tiles, meaning he subtracted. C and D already make no sense, but allow me to further explain. By him subtracting 5x from both sides, the equation turns into:

-4 = x + 4

By this point, he can just subtract 4 from both sides to find the value of x. But the question asks for why he did the first step. Therefore, it would be A.