In this lesson:
By the end of this lesson, you should be able to:
You already know how to evaluate expressions by substituting a number.
Today we answer that question by testing candidates.
An equation is a statement that two expressions are equal.
Only makes the equation true.
Test candidates :
The solution is .
Which value from makes true?
Substitute each candidate and evaluate — then advance for the answer.
An inequality like is true for all values greater than 3.
Values 2 and 4 pass — and any value less than 6 would also pass.
Test with candidates :
Values 6 and 7 pass — all values greater than 5 also pass.
Which values from make true?
Substitute each candidate and decide true or false — then advance.
✗
. Is ? No — equal is not less than. is not a solution.
Identify which values from the set are solutions:
Work through both substitutions — then advance for the answers.
, test :
Solution:
Problem 2: , test
Solution from this set: (all values above 5 work)
Identify all solutions from the given set:
Advance for the answers after working through each.
1. : gives 5 ✗ | gives 7 ✓ | gives 9 ✗ → Solution:
2. : gives 10 ✓ | gives 20 ✓ (≤ counts equal) | gives 30 ✗ → Solutions: ,
3. : gives 8 ✓ | gives 9 ✓ | gives 10 ✗ (< strict) | gives 11 ✗ → Solutions: ,
A variable is a placeholder for a number — not just a letter.
Test: Substitute a number, evaluate, decide true or false.
For : finding that works is not the full answer.
✓ Solving means finding values that make a statement true ✓ Equations: typically one solution from a candidate set ✓ Inequalities: a range — multiple values satisfy the condition
Watch out: Variables are number placeholders — not just letters Strict inequalities: boundary value does NOT count Inequalities: finding one solution does not finish the work
Coming next — 6.EE.B.6: Variables to represent real quantities
Click to begin the narrated lesson
Understand solving an equation or inequality as a process of answering a question