Question

Which of the following expressions could be interpreted as "a number times negative seven added to five equals two"?

-7 x - 5 = 2
5 + 7 x = 2
x - 7 + 5 = 2
5 - 7 x = 2

Answer 1

Let's break down the expression "a number times negative seven added to five equals two" step by step.

1. "a number" can be represented by the variable \( x \).
2. "times negative seven" means we multiply that number \( x \) by -7, giving us \( -7x \).
3. "added to five" means that we take the result of the multiplication and add 5, resulting in \( -7x + 5 \).
4. "equals two" indicates that this expression is equal to 2, which gives us the equation:

\[
-7x + 5 = 2
\]

Now, let's analyze the provided options:

1. **-7 x - 5 = 2**
This represents \(-7 \times -5 = 2\), which is incorrect because it implies a different expression (the multiplication of two numbers).

2. **5 + 7 x = 2**
This can be rewritten as \(5 + 7x = 2\), which does not match our equation.

3. **x - 7 + 5 = 2**
This simplifies to \(x - 2 = 2\) or \(x = 4\), which also does not match the original expression.

4. **5 - 7 x = 2**
This rearranges to \(5 - 7x = 2\), which can be rewritten as \(-7x + 5 = 2\) by rearranging terms, matching our derived equation.

Thus, the correct answer is:

**5 - 7 x = 2**