Question

nosaira solved an equation. her work is shown here: nosairas work 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. her work is incorrect. she distributed incorrectly. 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 moved terms across the equals sign incorrectly.

Explanation:

Step1: Check Distribution

For \(3(2x + 1)\), distributing gives \(6x + 3\). For \(2(x + 1)+1\), distributing \(2\) over \((x + 1)\) gives \(2x + 2\), then adding \(1\) gives \(2x + 3\). So steps 1 - 3 are correct.

Step2: Solve for \(x\)

From \(6x + 3 = 2x + 3\), subtract \(2x\) and \(3\) from both sides: \(6x - 2x + 3 - 3 = 0\), which simplifies to \(4x = 0\), then \(x = 0\). So the equation has a solution (\(x = 0\)), but Nosaira thought there was no solution. Her work (algebraic steps) is correct, but her interpretation of the solution is wrong.

Answer:

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