Question

Theo was asked to use the distributive property on the following problem on his algebra test: -2(3x-1). He writes that the answer is -6x - 2. however, his teacher told Theo his answer was incorrect. What could be the reason for his mistake.

A: Theo distributed a 2 to each term instead of -2

B: Theo forgot to subtract 3x - 1 before he distributed the -2

C: Theo did not distribute a -2 to the -1

D: Theo did not make any mistakes

Answer 1

Step-by-step explanation:

Theo's answer of -6x - 2 is incorrect because it does not correctly apply the distributive property to the expression -2(3x-1).

The distributive property states that for any numbers a, b, and c, the expression a(b + c) is equal to ab + ac. This property allows us to distribute the value of a to both b and c, which means that we can rewrite the expression as ab + ac instead of a(b + c).

In the expression -2(3x-1), the value of a is -2 and the values of b and c are 3x and -1, respectively. Applying the distributive property, we can rewrite the expression as (-2)(3x) + (-2)(-1). This simplifies to -6x + 2.

Therefore, Theo's answer is incorrect because he did not correctly apply the distributive property to the expression -2(3x-1). The correct answer is -6x + 2.

Answer 2

Answer: Choice C

Theo did not distribute a -2 to the -1

Step-by-step explanation:

This is a common mistake among students. Theo multiplied the outer -2 with 3x correctly to get -6x. But he forgot to multiply the outer -2 with the -1 inside to get +2. It appears he might have done 2*(-1) = -2

This means -2(3x-1) should be -6x+2 and NOT -6x-2

Another way to think about it is to think of 2(3x-1) = 6x-2, then flip the sign of each term. So the 6x flips to -6x, and the -2 flips to +2. This sign flip is because of the negative out front in -2(3x-1).

Or you can think of it like this

2(3x-1) = 6x-2

-2(3x-1) = -1*(6x-2)

-2(3x-1) = -1*6x - 1*(-2)

-2(3x-1) = -6x + 2