Question

Nosaira solved an equation. Her work is shown below: 3(2x + 1) = 2(x + 1) = 16x + 3 = 2x = 16x + 3 = 2x + 34x = 0x = 0. She determines the equation has no solution. Which of the following best describes Nosaira's work and answer? 1) Her work is correct, but there is one solution rather than no solution. 2) Her work is correct and her interpretation of the answer is correct. 3) Her work is incorrect. She distributed the terms incorrectly. 4) Her work is incorrect. She moved terms across the equals sign incorrectly.

Answer 1

After analysing Nosaira's work, it is clear that she distributed the terms incorrectly.

When distributing multiplication over addition in the brackets, the correct process should be as follows:

Starting with the equation 3(2x + 1),
we correctly distribute the 3 to both the 2x and the 1, which gives us 3*2x + 3*1 = 6x + 3.

Doing the same for the next equation 2(x + 1),
we distribute the 2 to both the x and the 1, giving us 2*x + 2*1 = 2x + 2.

Therefore, the correct answer to describe Nosaira's work and answer is option 3: "Her work is incorrect. She distributed the terms incorrectly."

Answer: 3) Her work is incorrect. She distributed the terms incorrectly.