Question

Noah solved an equation as shown below and found that the equation has infinitely many solutions.–3(x+4)+2x=2(x – 6)– 3x–3x– 12+2x= 2x– 12– 3x–x – 12= –x – 12Which explains whether Noah is correct?

a. Noah is correct because the two sides of the equation are equivalent expressions.
b. Noah is correct because if he continues the solution, the final solution will be x = –2C) Noah is not correct because the equivalent expressions mean that there is no solution.
d. Noah is not correct because he used the distributive property incorrectly.

Answer 1

–3(x+4) +2x = 2(x – 6) – 3x

–3x– 12 +2x = 2x– 12– 3x

–x – 12= –x – 12

0 = 0

Answer:

a. Noah is correct because the two sides of the equation are equivalent expressions.

Answer 2

Option c. Noah is not correct because the equivalent expressions mean that there is no solution.

Explanation:

Noah is correct:

Here are the steps:

The equation is stated as follows:

`-3(x+4)+ 2x = 2 (x-6) - 3x\\`

the expression gives:

`-3x-12+2x= 2x-12-3x\\ 0 = 0`

The equation has no solution.