Question

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Part 1
Peter ​says, "If you subtract 17 from my number and multiply the difference by negative 2​, the result is negative 42​." What is Peter​'s ​number?

Answer 1

Let's denote Peter's number as \( x \). According to the problem, we can set up the following equation based on the information provided:

1. Subtract 17 from Peter's number: \( x - 17 \)
2. Multiply the difference by -2: \( -2(x - 17) \)
3. Set this equal to -42:

\[
-2(x - 17) = -42
\]

Now, let's solve the equation step by step:

1. Distribute -2 on the left side:

\[
-2x + 34 = -42
\]

2. Subtract 34 from both sides:

\[
-2x = -42 - 34
\]
\[
-2x = -76
\]

3. Divide both sides by -2:

\[
x = \frac{-76}{-2}
\]
\[
x = 38
\]

So, Peter's number is \( \boxed{38} \).