Question

a student solved the following equation using the following steps:4(2−3x)=x−2(2x 1)4(2−3𝑥)=𝑥−2(2𝑥 1)8−3x=x−4x−28−3𝑥=𝑥−4𝑥−28−3x=−3x−28−3𝑥=−3𝑥−2answer: no solution(2 points)based on the student’s work, the equation was solved the equation solved correctly would show that it has skip to navigational

Answer 1

The student made an arithmetic error when expanding 4(2 − 3x). They wrote 4(2 − 3x) = 8 − 3x, but 4·(−3x) = −12x. Correct work:

4(2 − 3x) = x − 2(2x + 1)
8 − 12x = x − 4x − 2
8 − 12x = −3x − 2
Add 12x to both sides: 8 = 9x − 2
Add 2: 10 = 9x
x = 10/9

So the equation has one solution, x = 10/9.