Question

Write the expression that represents the phrase, "2 times the sum of 14 and a number"?

a) 2(x + 14)
b) 2x + 14
c) x + 28
d) 2x - 14

Answer 1

The expression that represents the phrase 2 times the sum of 14 and a number is option (a) 2(x + 14). So the correct one is option a.

Explanation:

In this expression, the variable x represents the unknown number. The phrase "the sum of 14 and a number" is represented as (x + 14), and multiplying this sum by 2 is denoted as 2(x + 14). Therefore, option (a) accurately captures the mathematical expression that corresponds to the given phrase.

The expression can be further expanded to provide a clearer understanding. Distributing the 2 to both terms inside the parentheses yields 2 * x + 2 * 14. This simplifies to 2x + 28, confirming that option (a) is equivalent to the original expression. The constant term 28 arises from multiplying 2 by 14, as specified in the phrase.

In conclusion, option (a) 2(x + 14) is the correct expression, as it correctly represents "2 times the sum of 14 and a number" by distributing the multiplication and capturing the sum of 14 and the variable x.

Answer 2

2(x + 14) represents the phrase, "2 times the sum of 14 and a number". So, Option A is correct.

Step-by-step explanation:

The expression "2 times the sum of 14 and a number" can be translated into algebraic terms by representing the unknown number as 'x.' The sum of 14 and the number 'x' is given by (x + 14), and multiplying this sum by 2 gives us the final expression 2(x + 14). Therefore, the correct answer is option (a).

Now, let's break down the expression and understand the logic behind it. We start with the sum of 14 and the unknown number (x):x + 14 . Multiplying this sum by 2 gives us the expression 2 (x + 14) . Distributing the 2 across the terms inside the parentheses results in 2x + 28 . So, the expression representing "2 times the sum of 14 and a number" is indeed (2(x + 14) , which matches with option (a).

In conclusion, option (a) accurately represents the given phrase in algebraic form. It reflects the process of multiplying the sum of 14 and a variable by 2. This understanding is crucial for correctly translating real-world scenarios into mathematical expressions, providing a foundation for solving a wide range of problems in algebra.