Algebraic Expressions — Understanding

Algebraic Expressions — Understanding. Practice questions to deepen understanding of algebraic expressions with conceptual understanding. Online math practice with full solutions and step-by-step explanations.

Algebraic Expressions — Understanding. Build deeper understanding of algebraic expressions: equivalence, simplification, and recognizing patterns.

30 questions

Question 1

3.33 pts

Substitution: Calculate the value of 2x + 3 when x = 5. Think of two groups of x plus 3 coins.

13

10

11

8

Explanation:

2 × 5 = 10, then add 3 to get 13. The expression means: two copies of x plus three.

Question 2

3.33 pts

Word description: What does the expression 4x + 1 represent? Imagine four copies of x then add 1 more.

4 times the number plus 1

1 times the number plus 4

x minus 4 plus 1

x divided by 4 plus 1

Explanation:

4x is the number multiplied by 4, and +1 is a constant addition.

Question 3

3.33 pts

Simplification: Simplify the expression x + 3x + 2. Think: 4 "x units" plus the constant 2.

4x + 2

3x + 2

2x + 4

5x + 2

Explanation:

Combine like terms: x + 3x = 4x, so 4x + 2.

Question 4

3.33 pts

Substitution: Find the value of 3(x − 2) when x = 6. Subtract 2 from x then multiply by 3.

12

6

9

3

Explanation:

(6 − 2) = 4, then 3 × 4 = 12.

Question 5

3.33 pts

Equivalent expression: Which expression is equivalent to x + x + x + x + 5?

4x + 5

5x + 4

x⁴ + 5

x + 9

Explanation:

There are four x terms, so 4x.

Question 6

3.33 pts

Substitution: Calculate 7 − x when x = 2. Imagine 7 coins, removing 2.

5

3

9

2

Explanation:

7 − 2 = 5.

Question 7

3.33 pts

Word description: What is "the number minus three times the number"?

x − 3x

3x − x

x + 3x

3 − x

Explanation:

x − 3x means we subtract three times the number from the number itself.

Question 8

3.33 pts

Equivalent expression: Which expression is equivalent to 2(x + 4)?

2x + 8

2x + 4

x + 6

4x + 2

Explanation:

Distributive property: multiply x by 2 and multiply 4 by 2.

Question 9

3.33 pts

Simplification: Simplify 9x − 2x + 1. Think: 9 "packs of x" minus 2 packs, plus 1.

7x + 1

11x + 1

7x − 1

9x − 3

Explanation:

9x − 2x = 7x.

Question 10

3.33 pts

Substitution: Calculate x² + x when x = 3. Square the number then add it.

12

9

6

3

Explanation:

3² = 9, then 9 + 3 = 12.

Question 11

3.33 pts

Word description: What does the expression 2x − 5 represent?

Twice a number minus 5

Half the number minus 5

5 times the number plus 2

5 minus twice the number

Explanation:

2x means doubled, and the subtraction reduces the result by 5.

Question 12

3.33 pts

Simplification: Combine like terms — x + 2 + 3x + 4.

4x + 6

x + 3x + 6

3x + 4

4x + 2

Explanation:

Combine: x + 3x = 4x and constants 2 + 4 = 6.

Question 13

3.33 pts

Substitution: Calculate 4(x − 1) when x = 10.

36

30

40

28

Explanation:

4 × (10 − 1) = 4 × 9 = 36.

Question 14

3.33 pts

Equivalent expression: What is equivalent to 6 + x + 2?

x + 8

6x + 2

x + 4

6 + x − 2

Explanation:

Combine constants: 6 + 2 = 8.

Question 15

3.33 pts

Substitution: Calculate 12 − 3x when x = 3.

3

6

9

12

Explanation:

12 − 3 × 3 = 12 − 9 = 3.

Question 16

3.33 pts

Simplification: Simplify 5x + x + x − 2.

7x − 2

6x − 2

7x + 2

5x + 3

Explanation:

5x + x + x = 7x.

Question 17

3.33 pts

Word description: "The number plus five, minus twice the number."

x + 5 − 2x

x − 5 − 2x

2x − 5

2(x − 5)

Explanation:

Direct verbal translation: x + 5 − 2x.

Question 18

3.33 pts

Substitution: Calculate x/2 + 6 when x = 8.

10

8

12

6

Explanation:

8/2 = 4, then 4 + 6 = 10.

Question 19

3.33 pts

Equivalence: What is equivalent to 3(x + 2)?

3x + 6

3x + 2

x + 6

6x + 3

Explanation:

Distributive property: 3x + 6.

Question 20

3.33 pts

Simplification: 8x − 5x + 4.

3x + 4

13x + 4

3x − 4

x + 4

Explanation:

8x − 5x = 3x.

Question 21

3.33 pts

Substitution: Find x² − 4 when x = 5.

21

25

9

1

Explanation:

5² = 25, then 25 − 4 = 21.

Question 22

3.33 pts

Description: What does the expression x + 12 represent?

The number plus 12

12 minus the number

The number divided by 12

12 times the number

Explanation:

Direct meaning: x plus the constant 12.

Question 23

3.33 pts

Simplification: Simplify x + x + x + 7.

3x + 7

4x + 3

x + 10

x³ + 7

Explanation:

3 copies of x plus 7.

Question 24

3.33 pts

Substitution: Calculate 4x − 1 when x = 9.

35

30

36

28

Explanation:

4 × 9 = 36, then 36 − 1 = 35.

Question 25

3.33 pts

Word description: Which of the following represents "five times the number then subtract 2"?

5x − 2

2x − 5

5(x − 2)

x/5 − 2

Explanation:

5x means five times, then minus 2.

Question 26

3.33 pts

Simplification: 6(x − 2) + 2.

6x − 10

6x − 8

4x − 2

6x + 2

Explanation:

6x − 12 + 2 = 6x − 10.

Question 27

3.33 pts

Substitution: Calculate x + 3 when x = 12.

15

10

14

9

Explanation:

12 + 3 = 15.

Question 28

3.33 pts

Simplification: x + 4 + 2x + 1.

3x + 5

2x + 4

x + 6

4x + 1

Explanation:

Combine: x + 2x = 3x and constants 4 + 1 = 5.

Question 29

3.33 pts

Substitution: Calculate (x + 1)(x − 1) when x = 4.

15

8

12

1

Explanation:

(4 + 1)(4 − 1) = 5 × 3 = 15.

Question 30

3.33 pts

Description: What does the expression 2x + x + 10 represent?

3x + 10

2x + 1 + 10

x³ + 10

x + 12

Explanation:

Combine like terms: 2x + x = 3x.