What you’ll learn
Test whether a value satisfies an equation.
Key idea
Evaluate every left-side term; zero difference certifies equality and a nonzero difference refutes it.
Evaluate the full left side; zero residual proves the proposed input satisfies equality, while nonzero residual disproves it.
Worked example
Enter the exact value or ordered values in the format requested below.
Test x=6 in 2x+1=11. Enter left side minus right side; zero certifies a solution.
- At x=6, the complete left side is 2×6+1=13.
- Left minus right is 13-11=2; hence x=6 is not a solution.
Answer: 2
Quick Check
Evaluate a worked attempt at test whether a value satisfies an equation, identify the first invalid step, and provide the correction.
A student tests x=5 in 2x+2=12: Step 1, substitute 2(5)+2. Step 2, call the complete left side 10, omitting the addition. Locate the first invalid step and correct the solution decision.