Difficulty: Medium
Correct Answer: x ÷ + =
Explanation:
Introduction / Context:
We must choose an ordered sequence of operators to make a numeric statement true. This requires both precedence awareness and testing of plausible combinations.
Given Data / Assumptions:
Concept / Approach:
Substitute each option in order and evaluate the left-hand side (LHS). The correct option should yield an identity when compared to the right-most number.
Step-by-Step Solution:
Try Option B: “× ÷ + =”.Substitute: 5 × 6 ÷ 5 + 8 = 14.Compute precedence: 5 × 6 = 30; 30 ÷ 5 = 6; then 6 + 8 = 14.The equality holds, so Option B is correct.
Verification / Alternative check:
Option A: 5 + 6 − 5 × 8 = 14 ⇒ 5 + 6 − 40 = −29 ≠ 14.Option C: 5 ÷ 6 × 5 = 8 − 14 ⇒ LHS ≈ 4.166…, RHS = −6; false.Option D: 5 + 6 × 5 − 8 ÷ 14 ⇒ 5 + 30 − 8 ÷ 14 ≈ 34.43; not a clean equality to 14.
Why Other Options Are Wrong:
They mis-balance the expression through a large product or an ill-placed subtraction/division that prevents the LHS from reaching 14.
Common Pitfalls:
Executing left-to-right without applying ×/÷ before +/−; or mistakenly trying to “compute” the equality symbol as an operator.
Final Answer:
x ÷ + = gives the true equation 5 × 6 ÷ 5 + 8 = 14.
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