What is the solution to the equation 2x + 3 = 7?

1. INFER the solving strategy

• Given: \(\mathrm{2x + 3 = 7}\)
• Goal: Find the value of x that makes this equation true
• Strategy: Isolate x by "undoing" the operations around it in reverse order
• We see x is multiplied by 2, then 3 is added, so we'll subtract 3 first, then divide by 2

2. SIMPLIFY by removing the constant term

• Subtract 3 from both sides: \(\mathrm{2x + 3 - 3 = 7 - 3}\)
• This gives us: \(\mathrm{2x = 4}\)
• Now x is only multiplied by 2

3. SIMPLIFY by removing the coefficient

• Divide both sides by 2: \(\mathrm{2x \div 2 = 4 \div 2}\)
• This gives us: \(\mathrm{x = 2}\)

Answer: C. 2

Why Students Usually Falter on This Problem

Most Common Error Path:

Incomplete SIMPLIFY execution: Students correctly find that \(\mathrm{2x = 4}\) but stop there without completing the final division step.

They see "\(\mathrm{2x = 4}\)" and think this IS the solution, not realizing they need to find the value of x itself, not 2x. This leads them to select Choice D (4).

Second Most Common Error:

Computational errors during SIMPLIFY: Students understand the correct strategy but make arithmetic mistakes during the subtraction or division steps.

For example, they might incorrectly calculate 7 - 3 or make division errors, leading to wrong values. This may lead them to select Choice A (1) or Choice B (1.5).

The Bottom Line:

This problem tests whether students can systematically execute a two-step algebraic process without stopping prematurely or making computational errors. The key insight is that finding "\(\mathrm{2x = 4}\)" is not the final answer - you must continue to isolate x completely.