x + 40 = 95 What value of x is the solution to the given equation?...

1. INFER the solving strategy

• Given: \(\mathrm{x + 40 = 95}\)
• Goal: Find the value of x that makes this equation true
• Strategy: Isolate x by undoing the addition of 40

2. INFER the correct operation

• Since 40 is being added to x, we need to subtract 40 to undo this
• Apply the equality principle: subtract 40 from both sides

\(\mathrm{x + 40 = 95}\)

\(\mathrm{x + 40 - 40 = 95 - 40}\)

\(\mathrm{x = 55}\)

Answer: 55

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Using the wrong operation by adding instead of subtracting

Students sometimes think "I see +40 and 95, so I should add them together" without understanding that solving means undoing the operation that's being performed on x. They might calculate:

\(\mathrm{x = 95 + 40 = 135}\)

This leads to an incorrect answer that would make the original equation false (\(\mathrm{135 + 40 \neq 95}\)).

The Bottom Line:

The key insight is recognizing that solving an equation means performing the inverse (opposite) operation to isolate the variable. Addition problems require subtraction to solve, and subtraction problems require addition to solve.