Let's break down the expression "a number times negative seven added to five equals two" step by step.
- "a number" can be represented by the variable \( x \).
- "times negative seven" means we multiply that number \( x \) by -7, giving us \( -7x \).
- "added to five" means that we take the result of the multiplication and add 5, resulting in \( -7x + 5 \).
- "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:
-
-7 x - 5 = 2
This represents \(-7 \times -5 = 2\), which is incorrect because it implies a different expression (the multiplication of two numbers). -
5 + 7 x = 2
This can be rewritten as \(5 + 7x = 2\), which does not match our equation. -
x - 7 + 5 = 2
This simplifies to \(x - 2 = 2\) or \(x = 4\), which also does not match the original expression. -
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
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