Learning Goal: Understand that solving an equation or inequality means finding values that make it true, tested by substitution.
Vocabulary
equationA math sentence stating two expressions are equal, using an equal sign, like x + 4 = 9.
inequalityA math sentence comparing two expressions with <, >, ≤, or ≥.
solutionA value of the variable that makes the equation or inequality true.
substituteReplace the variable with a number to check if the sentence is true.
What You Need to Know
A solution is any value that makes the equation or inequality TRUE when substituted.
To check, replace the variable with the value and see if both sides match (or the comparison holds).
An equation usually has one solution; an inequality can have many solutions.
Example: x = 5 is a solution to x + 3 = 8 because 5 + 3 = 8 is true.
If substituting gives a false statement, that value is NOT a solution.
For inequalities, test whether the value satisfies < or > (for example, 7 > 4 is true).
Worked Example I Do — watch how it works
Is x = 6 a solution to the equation 2x − 1 = 11?
Step 1. Substitute 6 for x: 2(6) − 1.
Step 2. Evaluate the left side: 12 − 1 = 11.
Step 3. Compare to the right side: 11 = 11 is true, so x = 6 works.
Answer: Yes, x = 6 is a solution.
Guided Practice We Do — try it together
1. Is n = 4 a solution to n + 7 = 11?
💡 Hint: Substitute 4 and check if both sides equal.
2. Is x = 3 a solution to the inequality x > 5?
💡 Hint: Check whether 3 is greater than 5.
3. Is y = 10 a solution to y − 4 = 5?
💡 Hint: Substitute and compare both sides.
Independent Practice You Do — show your work
1. Is x = 8 a solution to x + 5 = 13?
2. Is m = 2 a solution to 4m = 12?
3. Is x = 9 a solution to x > 6?
4. Is p = 5 a solution to 3p − 2 = 13?
5. Is n = 1 a solution to n < 1?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.B.5.
Item 1Selected Response6.EE.B.5
Which value of x makes x + 6 = 14 true?
Select the correct answer.
Item 2Selected Response6.EE.B.5
Which value is a solution to the inequality x > 7?
Select the correct answer.
Item 3Constructed Response6.EE.B.5
A bus holds 30 students. The expression 30 − s shows empty seats. Is s = 25 a solution to 30 − s = 5?
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
Yes
Independent 2
No; 4(2) = 8, not 12
Independent 3
Yes
Independent 4
Yes; 3(5) − 2 = 13
Independent 5
No; 1 is not less than 1
Item 1 · 6.EE.B.5
B — Substituting 8 gives 8 + 6 = 14, a true statement.
Item 2 · 6.EE.B.5
D — Only 9 is greater than 7. Note 7 is not a solution because 7 > 7 is false.
Item 3 · 6.EE.B.5
Yes; 30 − 25 = 5. — Substituting 25 gives 30 − 25 = 5, which is true.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.B.5