Question

match the correct mathematical expression with each phrase. an answer choice may be used more than once or not at all. twice a number, increased by five twice the difference of a number and five twice the sum of a number and five five decreased by twice a number five less than twice a number twice a number less five 2x - 5 2(x - 5) 5 - 2x 2x + 5 2(x + 5)

Explanation:

1. "twice a number, increased by five"

Let the number be \( x \). "Twice a number" is \( 2x \), and "increased by five" means adding 5 to \( 2x \). So the expression is \( 2x + 5 \).

2. "twice the difference of a number and five"

"the difference of a number and five" is \( x - 5 \), and "twice" that difference means multiplying by 2. So the expression is \( 2(x - 5) \).

3. "twice the sum of a number and five"

"the sum of a number and five" is \( x + 5 \), and "twice" that sum means multiplying by 2. So the expression is \( 2(x + 5) \).

4. "five decreased by twice a number"

"twice a number" is \( 2x \), and "five decreased by" that means subtracting \( 2x \) from 5. So the expression is \( 5 - 2x \).

5. "five less than twice a number"

"twice a number" is \( 2x \), and "five less than" that means subtracting 5 from \( 2x \). So the expression is \( 2x - 5 \).

6. "twice a number less five"

"twice a number" is \( 2x \), and "less five" means subtracting 5 from \( 2x \). So the expression is \( 2x - 5 \).

Answer:

• twice a number, increased by five: \( 2x + 5 \)
• twice the difference of a number and five: \( 2(x - 5) \)
• twice the sum of a number and five: \( 2(x + 5) \)
• five decreased by twice a number: \( 5 - 2x \)
• five less than twice a number: \( 2x - 5 \)
• twice a number less five: \( 2x - 5 \)