8x = 88 What value of x is the solution to the given equation?...

1. INFER what operation will isolate x

• Given equation: \(8\mathrm{x} = 88\)
• The variable x is being multiplied by 8
• To isolate x, I need to use the inverse operation of multiplication, which is division
• I should divide both sides by 8

2. SIMPLIFY by dividing both sides by 8

• \(8\mathrm{x} \div 8 = 88 \div 8\)
• The left side simplifies: \(8\mathrm{x} \div 8 = \mathrm{x}\)
• The right side: \(88 \div 8 = 11\)
• Therefore: \(\mathrm{x} = 11\)

Answer: A. 11

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse this equation with similar-looking equations and choose the wrong operation. Instead of recognizing they need to divide by 8, they might:

• Add 8 to both sides (thinking of \(\mathrm{x} + 8 = 88\)), getting x = 96
• Subtract 8 from both sides (thinking of \(\mathrm{x} - 8 = 88\)), getting x = 80
• Multiply both sides by 8 (thinking of \(\mathrm{x}/8 = 88\)), getting x = 704

This confusion about which inverse operation to use may lead them to select Choice B (80), Choice C (96), or Choice D (704).

The Bottom Line:

The key challenge is recognizing that 8x means "8 times x" and therefore requires division to isolate x. Students often get confused between different equation types and apply the wrong inverse operation.