Let’s go through each problem one by one, step by step.
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Problem 1: “5 more than 3 times a number”
- “A number” → let’s call it
x
- “3 times a number” →
3x
- “5 more than” that → add 5 to 3x →
3x + 5 or
5 + 3x (same thing)
Look at the options:
- A: 3 + n + 5 → not matching
- B: 5 + 3 x 10 → has a 10? No, we don’t know the number is 10
- C: 8 → just a number, no variable
- D: 5 + 3x → YES! This matches.
✔ Answer for #1:
D
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Problem 2: “a number tripled is equal to 18”
- “A number” → let’s say
n
- “Tripled” → multiplied by 3 →
3n
- “Is equal to 18” →
= 18
So:
3n = 18
Check options:
- A: 3n = 18 → perfect match
- B: 18 ÷ 3 = n → this solves it, but doesn’t express the phrase as given
- C: 6 → just the answer, not the expression
- D: 3 × 6 = 18 → again, solved version, not the algebraic expression of the phrase
The question asks for the *algebraic expression* for the phrase — so we want the equation before solving.
✔ Answer for #2:
A
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Problem 3: “Twice x, decreased by 9”
- “Twice x” →
2x
- “Decreased by 9” → subtract 9 →
2x - 9
Options:
- A: 2 + x - 9 → wrong, that’s “2 plus x minus 9”
- B: 2x - 9 → correct!
- C: 9 - 2x → backwards
- D: 2x / 9 → division? No
✔ Answer for #3:
B
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Problem 4: “six feet less than the width (use w for width)”
- Width =
w
- “Six feet less than” → subtract 6 from width →
w - 6
Note: “less than” means you subtract FROM the first thing mentioned. So “6 less than w” = w - 6
Options:
- A: 6/w → division? No
- B: 6 - w → that’s “w less than 6”, opposite
- C: w - 6 → yes!
- D: w/6 → division? No
✔ Answer for #4:
C
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Problem 5: Simplify x + x + x + x
That’s four x’s added together →
4x
Options:
- A: x+4 → no, that’s x plus 4
- B: 4x → yes!
- C: 4 - x → subtraction? No
- D: x → only one x? No
✔ Answer for #5:
B
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Problem 6: Simplify 3x + 3 - 1
Combine like terms:
- The constants: 3 - 1 =
2
- The variable term: still
3x
So:
3x + 2
Options:
- A: 3x + 4 → too big
- B: 3x + 2 → correct!
- C: 5x → where did 5 come from?
- D: x - 1 → nope
✔ Answer for #6:
B
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Final Answer:
1. D
2. A
3. B
4. C
5. B
6. B
Parent Tip: Review the logic above to help your child master the concept of 9th grade algebra practice.
