Question

potential errors
nosaira solved an equation. her work is shown below:

1. $3(2x + 1) = 2(x + 1) + 1$
2. $6x + 3 = 2x + 2 + 1$
3. $6x + 3 = 2x + 3$
4. $4x = 0$
5. $x = 0$

she determines the equation has no solution.
which best describes nosaira’s work and answer?

• her work is correct, but there is one solution rather than no solution.
• her work is correct and her interpretation of the answer is correct.
• her work is incorrect. she distributed incorrectly.
• her work is incorrect. she moved terms across the equals sign incorrectly.

Explanation:

Step1: Verify distribution step

Left side: $3(2x+1)=6x+3$, Right side: $2(x+1)+1=2x+2+1$. Both are correct.

Step2: Simplify right-hand side

$2x+2+1=2x+3$. This step is correct.

Step3: Isolate variable terms

Subtract $2x+3$ from both sides: $6x+3-(2x+3)=2x+3-(2x+3)$ → $4x=0$. This step is correct.

Step4: Solve for x

$x=\frac{0}{4}=0$. The equation has one solution $x=0$, but Nosaira incorrectly claimed no solution.

Answer:

Her work is correct, but there is one solution rather than no solution.