The function h is defined by \(\mathrm{h(x) = 3x + 7}\). For what value of x is \(\mathrm{h(x) = -8}\)?-15-5-{1/3}1/3

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{h(x) = 3x + 7}\)
  • Need to find: the value of x when \(\mathrm{h(x) = -8}\)
• This means we need to solve: \(\mathrm{3x + 7 = -8}\)

2. SIMPLIFY to solve for x

• Start with: \(\mathrm{3x + 7 = -8}\)
• Subtract 7 from both sides: \(\mathrm{3x = -8 - 7}\)
• Calculate: \(\mathrm{3x = -15}\)
• Divide both sides by 3: \(\mathrm{x = -5}\)

3. Verify the solution

• Check: \(\mathrm{h(-5) = 3(-5) + 7}\)
  \(\mathrm{= -15 + 7}\)
  \(\mathrm{= -8}\) ✓

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: When subtracting 7 from both sides, students incorrectly calculate \(\mathrm{3x = -8 + 7 = -1}\) instead of \(\mathrm{3x = -8 - 7 = -15}\).

This happens because they think "move 7 to the other side" means just changing its position, forgetting that subtracting 7 from both sides requires: \(\mathrm{-8 - 7}\).

This leads them to get \(\mathrm{x = -\frac{1}{3}}\) and select Choice C (-1/3).

Second Most Common Error:

Insufficient SIMPLIFY completion: Students correctly get \(\mathrm{3x = -15}\) but then make an error in the final division, perhaps writing \(\mathrm{x = -15}\) instead of \(\mathrm{x = -\frac{15}{3} = -5}\).

This causes them to select Choice A (-15).

The Bottom Line:

This problem tests whether students can systematically work through the algebra without rushing. The key is carefully tracking signs when moving terms across the equals sign and completing each arithmetic step accurately.