Question
Solve using the addition principle. Don't forget to check. \( -48+x=-75 \)
Ask by Griffin Martin. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -27 \)
Solution
To solve the equation \( -48 + x = -75 \) using the **addition principle**, follow these steps:
1. **Objective:** Isolate the variable \( x \).
2. **Apply the Addition Principle:** Add 48 to both sides of the equation to eliminate the \(-48\) on the left side.
\[
-48 + x + 48 = -75 + 48
\]
3. **Simplify Both Sides:**
\[
x = -27
\]
4. **Check the Solution:** Substitute \( x = -27 \) back into the original equation to verify.
\[
-48 + (-27) = -75
\]
\[
-75 = -75 \quad \text{✓}
\]
The left side equals the right side, confirming that the solution is correct.
**Final Answer:**
\[
x = -27
\]
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Simplify this solution The Deep Dive
To solve the equation \( -48 + x = -75 \) using the addition principle, we want to isolate \( x \). We can do this by adding \( 48 \) to both sides of the equation: \[ -48 + x + 48 = -75 + 48 \] This simplifies to: \[ x = -27 \] Now, let’s check our solution by substituting \( x \) back into the original equation: \[ -48 + (-27) = -75 \] Calculating the left side gives: \[ -48 - 27 = -75 \] This confirms that our solution is correct. So, \( x = -27 \) is indeed the right answer!
