Question

Identify the equation that is solved correctly given the following written directions: subtract 5 from both sides of the equation. Then, multiply both sides of the equation by negative 2. The final answer is x = 8.(1 point)
Responses

x2+5=1
x over 2 plus 5 is equal to 1

x−2+5=1
x over negative 2 plus 5 is equal to 1

x2−5=1
x over 2 minus 5 is equal to 1

x−2−5=1

Answer 1

To find the equation that leads to the final answer of \(x = 8\) after following the given directions, we can reverse-engineer the steps.

1. Start with the final answer: \(x = 8\).
2. The last operation performed was multiplying both sides by \(-2\). To find the value before this operation, we need to divide by \(-2\):

\[
8 \div -2 = -4
\]

3. Before we multiplied by \(-2\), we must have subtracted \(5\) from both sides. So, we need to add \(5\) to \(-4\):

\[
-4 + 5 = 1
\]

Now, we know that before we performed the operations, we had the equation:

\[
x - 5 = 1
\]

Next, let's see if any of the given options yield this result when we apply the operations.

1. **For \(x^2 + 5 = 1\)**:
\[
x^2 + 5 - 5 = 1 - 5 \Rightarrow x^2 = -4 \quad (\text{not applicable})
\]

2. **For \(x - 2 + 5 = 1\)**:
\[
x - 2 + 5 - 5 = 1 - 5 \Rightarrow x - 2 = -4 \Rightarrow x = -2 + 4 = 2 \quad (\text{not applicable})
\]

3. **For \(x^2 - 5 = 1\)**:
\[
x^2 - 5 + 5 = 1 + 5 \Rightarrow x^2 = 6 \quad (\text{not applicable})
\]

4. **For \(x - 2 - 5 = 1\)**:
\[
x - 2 - 5 + 5 = 1 + 5 \Rightarrow x - 2 = 6 \Rightarrow x = 6 + 2 = 8 \quad (\text{this matches})
\]

Only the last option leads to the correct answer, so the correct equation is:

\[
x - 2 - 5 = 1
\]