Question 1 — Multiple Choice
Is x = 4 a solution to the equation
3x + 1 = 13?
Strategy: Replace x with
4, then compute the left side. Does it equal 13?
Substitute: 3(4) + 1 = 12 + 1 = ? Compare to 13.
✓Correct! 3(4) + 1 = 12 + 1 = 13. Both sides equal 13, so x = 4 is a
solution.
✗Substitute 4 for x: 3(4) + 1 = 12 + 1 = 13 ✓. The answer is
A — x = 4 is a solution.
Question 2 — True or False
True or False: An equation always has an equals sign.
Remember: An equation uses
the = sign. An inequality uses <, >,
≤, or ≥. An expression has no
comparison symbol at all.
Think about what makes an equation different from an expression or an
inequality.
✓Correct! By definition, an equation is a math sentence with an
equals sign showing two expressions are equal.
✗The statement is true. An equation must have an
equals sign (=). That is what makes it an equation.
Question 3 — Fill In
Find the value that makes the equation true:
Think: What number plus 9 equals 15? You can count up
from 9 or subtract: 15 − 9 = ?
Use the inverse operation: 15 − 9 = ?
+ 9 = 15
✓Correct! 6 + 9 = 15. The value 6 makes the equation true.
✗15 − 9 = 6. The missing value is 6 because 6
+ 9 = 15.
Question 4 — Multiple Choice
Solve: n + 7 = 20
Inverse operation: Addition and subtraction undo each
other. To get n alone, subtract 7 from both sides.
n + 7 = 20 → n = 20 − 7
✓Correct! n + 7 = 20 → n = 20 − 7 = 13. Check: 13 + 7 =
20 ✓
✗Subtract 7 from both sides: n = 20 − 7 = 13.
The answer is B.
Question 5 — Fill In
Solve: x − 12 = 8
Inverse operation: Subtraction is undone by addition.
Add 12 to both sides to isolate x.
x − 12 = 8 → x = 8 + 12
x =
✓Correct! x = 8 + 12 = 20. Check: 20 − 12 = 8 ✓
✗Add 12 to both sides: x = 8 + 12 = 20. Check: 20
− 12 = 8 ✓
Question 6 — Multiple Choice
Which equation represents:
"15 more than a number is 42"?
Key phrase: "15 more than" means
add 15. "A number" is the variable. "Is"
means equals (=).
"15 more than a number" → n + 15. "Is 42" → = 42.
✓Correct! "15 more than a number" translates to n + 15, and "is 42"
means = 42. So: n + 15 = 42.
✗"More than" means addition. The correct equation is
C: n + 15 = 42.
Question 7 — Fill In
Solve: 6m = 54
Inverse operation: 6m means 6 times
m. To undo multiplication,
divide both sides by 6.
6m = 54 → m = 54 ÷ 6
m =
✓Correct! m = 54 ÷ 6 = 9. Check: 6(9) = 54 ✓
✗Divide both sides by 6: m = 54 ÷ 6 = 9.
Check: 6(9) = 54 ✓
Question 8 — Multiple Choice
Solve: y ÷ 5 = 9
Inverse operation: Division is undone by
multiplication. Multiply both sides by 5.
y ÷ 5 = 9 → y = 9 × 5
✓Correct! y = 9 × 5 = 45. Check: 45 ÷ 5 = 9
✓
✗Multiply both sides by 5: y = 9 × 5 = 45.
The answer is C.
Question 9 — Multiple Choice
The total cost is $72 for
n equally-priced items at $8 each. Which
equation models this, and what is n?
Set up the equation: Each item costs $8 and there are
n items. Total cost = price per item × number of items.
So: 8n = 72.
8n = 72 → n = 72 ÷ 8
✓Correct! 8n = 72 → n = 72 ÷ 8 = 9. There are 9 items.
Check: 8(9) = 72 ✓
✗Price × quantity = total: 8n = 72. Divide: n = 72 ÷ 8
= 9. The answer is A.
Question 10 — Multiple Choice
Which inequality means "at least 18 years old"?
Key phrase:
"At least" means the value can be 18 or
greater. That is the ≥ symbol (greater
than or equal to).
"At least 18" means 18 is the minimum allowed value. The age can be
18, 19, 20, ...
✓Correct! "At least 18" means 18 or older, which is a ≥ 18.
✗"At least" includes the number itself. The answer is
B: a ≥ 18 (greater than or equal to).
Question 11 — True or False
True or False:
x > 5 includes the value 5.
Symbol check: > means
"strictly greater than" — the number itself is NOT included.
Only ≥ would include 5.
Is 5 greater than 5? Or is 5 equal to 5?
✓Correct! x > 5 means strictly greater than 5. The value 5 itself
is not included.
✗This is false. The > symbol means "strictly
greater than," so 5 is not a solution to x > 5.
Question 12 — Fill In
Write the inequality: "Fewer than 30 students"
Key phrase:
"Fewer than" means less than. Which symbol
means "less than"?
"Fewer than" = "less than" = the < symbol.
n
30
✓Correct! "Fewer than 30" means n < 30.
✗"Fewer than" means less than. The answer is <,
giving us n < 30.
Question 13 — Multiple Choice
Which value is a solution to
x + 3 > 10?
Strategy: Substitute each value for x. Add
3. Is the result greater than 10?
First, solve: x + 3 > 10 → x > 7. Which choices are greater
than 7?
✓Correct! 8 + 3 = 11, and 11 > 10 is true. So x = 8 is a
solution.
✗x > 7 is needed. Only 8 > 7. Check: 8 + 3 = 11 > 10
✓. The answer is C.
Question 14 — True or False
True or False:
An inequality can have infinitely many solutions.
Think about it: The inequality x > 5 includes 6,
7, 8, 9, ... and also 5.1, 5.01, 5.001, ... Does the list ever end?
Compare: an equation like x + 3 = 10 has one solution. An inequality
like x > 5 has how many?
✓Correct! Unlike equations (which usually have one solution),
inequalities have infinitely many values that make them true.
✗This is true. For example, x > 5 is true for 6,
7, 100, 5.5, and infinitely many more values.
Question 15 — Drag and Drop
Sort each value into "Solution" or
"Not a Solution" for the inequality
n ≤ 6.
Remember: n ≤ 6 means n
is less than or equal to 6. So 6 counts! Any number that is 6
or smaller is a solution.
Check each number: is it 6 or less? If yes, it is a solution. If it is
greater than 6, it is not.
✓All correct! 3, 6, and 0 are all ≤ 6. The values 7, 10, and 15
are greater than 6 and are not solutions.
✗Check each number: is it ≤ 6? Solutions: 0, 3, 6. Not solutions:
7, 10, 15. Remember, 6 is included because of the ≤ symbol!
Your Results
Unit 8: Equations & Inequalities Review