If \(2\mathrm{x} + 6 = 90 - (4\mathrm{x} - 30)\), what is the value of 3x?[FIB]

1. SIMPLIFY the right side of the equation

• Given: \(\mathrm{2x + 6 = 90 - (4x - 30)}\)
• Expand the right side using distributive property:
  • \(\mathrm{90 - (4x - 30) = 90 - 4x + 30 = 120 - 4x}\)
• Equation becomes: \(\mathrm{2x + 6 = 120 - 4x}\)

2. INFER the strategy to solve for x

• We need all x terms on one side and constants on the other
• Add 4x to both sides to collect the x terms

3. SIMPLIFY by combining like terms

• \(\mathrm{2x + 4x + 6 = 120 - 4x + 4x}\)
• \(\mathrm{6x + 6 = 120}\)

4. SIMPLIFY to isolate the variable term

• Subtract 6 from both sides: \(\mathrm{6x = 114}\)
• Divide both sides by 6: \(\mathrm{x = 19}\)

5. INFER what the question is actually asking

• The question asks for 3x, not just x
• Calculate: \(\mathrm{3x = 3(19) = 57}\)

Answer: 57

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make sign errors when expanding \(\mathrm{90 - (4x - 30)}\), often getting \(\mathrm{90 - 4x - 30 = 60 - 4x}\) instead of \(\mathrm{90 - 4x + 30 = 120 - 4x}\).

This leads them to solve \(\mathrm{2x + 6 = 60 - 4x}\), which gives \(\mathrm{6x = 54}\), so \(\mathrm{x = 9}\), and therefore \(\mathrm{3x = 27}\). This would result in an incorrect answer of 27.

Second Most Common Error:

Poor attention to the final question: Students correctly solve for \(\mathrm{x = 19}\), but then forget that the question asks for 3x and submit 19 as their final answer.

This causes them to provide 19 instead of the correct answer 57.

The Bottom Line:

This problem tests both careful algebraic manipulation and reading comprehension. Success requires computational accuracy with parentheses and attention to what's actually being asked in the final step.