Question

algebraic expressions challenge
match each algebraic expression with its equivalent written expression.

1. a number subtracted from 2
2. 2 groups of the sum of a number and 2
3. a number times itself
4. 2 more than a number
5. split the sum of 2 and a number into 2 equal groups
6. half a number
7. twice the difference of a number and 2
8. 2 more than the product of a number and 2
9. 2 less than a number
10. 2 removed from 2 of a number
11. double a number

expressions: ( x + 2 ), ( x - 2 ), ( 2 - x ), ( 2x ), ( \frac{x}{2} ), ( 2x + 2 ), ( 2x - 2 ), ( \frac{x + 2}{2} ), ( 2(x + 2) ), ( 2(x - 2) ), ( x^2 )

Explanation:

1. A number subtracted from 2

• Explanation: "A number subtracted from 2" means \( 2 - x \) (where \( x \) is the number).
• Answer: \( 2 - x \)

2. 2 groups of the sum of a number and 2

• Explanation: "The sum of a number and 2" is \( x + 2 \), and "2 groups of" that sum means multiplying by 2: \( 2(x + 2) \).
• Answer: \( 2(x + 2) \)

3. A number times itself

• Explanation: A number times itself is the number squared, so \( x \times x = x^2 \).
• Answer: \( x^2 \)

4. 2 more than a number

• Explanation: "2 more than a number" means adding 2 to the number: \( x + 2 \).
• Answer: \( x + 2 \)

5. Split the sum of 2 and a number into 2 equal groups

• Explanation: "The sum of 2 and a number" is \( x + 2 \), and "split into 2 equal groups" means dividing by 2: \( \frac{x + 2}{2} \).
• Answer: \( \frac{x + 2}{2} \)

6. Half a number

• Explanation: "Half a number" means dividing the number by 2: \( \frac{x}{2} \).
• Answer: \( \frac{x}{2} \)

7. Twice the difference of a number and 2

• Explanation: "The difference of a number and 2" is \( x - 2 \), and "twice" that difference means multiplying by 2: \( 2(x - 2) \).
• Answer: \( 2(x - 2) \)

8. 2 more than the product of a number and 2

• Explanation: "The product of a number and 2" is \( 2x \), and "2 more than" that product means adding 2: \( 2x + 2 \).
• Answer: \( 2x + 2 \)

9. 2 less than a number

• Explanation: "2 less than a number" means subtracting 2 from the number: \( x - 2 \).
• Answer: \( x - 2 \)

10. 2 removed from 2 of a number

• Explanation: "2 of a number" is \( 2x \), and "2 removed from" that means subtracting 2: \( 2x - 2 \).
• Answer: \( 2x - 2 \)

11. Double a number

• Explanation: "Double a number" means multiplying the number by 2: \( 2x \).
• Answer: \( 2x \)

Answer:

1. A number subtracted from 2

• Explanation: "A number subtracted from 2" means \( 2 - x \) (where \( x \) is the number).
• Answer: \( 2 - x \)

2. 2 groups of the sum of a number and 2

• Explanation: "The sum of a number and 2" is \( x + 2 \), and "2 groups of" that sum means multiplying by 2: \( 2(x + 2) \).
• Answer: \( 2(x + 2) \)

3. A number times itself

• Explanation: A number times itself is the number squared, so \( x \times x = x^2 \).
• Answer: \( x^2 \)

4. 2 more than a number

• Explanation: "2 more than a number" means adding 2 to the number: \( x + 2 \).
• Answer: \( x + 2 \)

5. Split the sum of 2 and a number into 2 equal groups

• Explanation: "The sum of 2 and a number" is \( x + 2 \), and "split into 2 equal groups" means dividing by 2: \( \frac{x + 2}{2} \).
• Answer: \( \frac{x + 2}{2} \)

6. Half a number

• Explanation: "Half a number" means dividing the number by 2: \( \frac{x}{2} \).
• Answer: \( \frac{x}{2} \)

7. Twice the difference of a number and 2

• Explanation: "The difference of a number and 2" is \( x - 2 \), and "twice" that difference means multiplying by 2: \( 2(x - 2) \).
• Answer: \( 2(x - 2) \)

8. 2 more than the product of a number and 2

• Explanation: "The product of a number and 2" is \( 2x \), and "2 more than" that product means adding 2: \( 2x + 2 \).
• Answer: \( 2x + 2 \)

9. 2 less than a number

• Explanation: "2 less than a number" means subtracting 2 from the number: \( x - 2 \).
• Answer: \( x - 2 \)

10. 2 removed from 2 of a number

• Explanation: "2 of a number" is \( 2x \), and "2 removed from" that means subtracting 2: \( 2x - 2 \).
• Answer: \( 2x - 2 \)

11. Double a number

• Explanation: "Double a number" means multiplying the number by 2: \( 2x \).
• Answer: \( 2x \)