Question

Compare Solution Methods for Multi-Step Equations quick check when solving the equation -1/2(x+10)=-3 identify the operation that should be done first

Answer 1

To solve the equation \(-\frac{1}{2}(x + 10) = -3\), we can compare different approaches. However, the first operation we need to identify is dealing with the fraction outside the parentheses.

**Step 1: Identify the First Operation**

We can begin by eliminating the negative fraction. To isolate the group of terms in parentheses, we can multiply both sides of the equation by -2, which is the reciprocal of \(-\frac{1}{2}\). This will effectively eliminate the fraction from the left side.

**Equation:**
\[
-\frac{1}{2}(x + 10) = -3
\]

**First operation: Multiply both sides by -2**
\[
(x + 10) = 6
\]

After this step, you can proceed to solve for \(x\) by subtracting 10 from both sides:

\[
x = 6 - 10
\]
\[
x = -4
\]

**Solution Summary:**
1. Multiply both sides by -2 to eliminate the fraction.
2. Solve for \(x\).

This approach efficiently simplifies the equation, with the first operation being the multiplication by -2.