Question

Given the equation 5 + x -12 =x - 7

Part A. Solve the equation 5 + x -12 =x - 7
. In your final answer, be sure to state the solution and include all of your work.

Part B. Use the values x=-4, 0, 5
to verify your solution to the equation 5 + x -12 =x - 7
. In your final answer, include all of your calculations.

Answer 1

Let's solve the equation step by step.

### Part A: Solve the equation \(5 + x - 12 = x - 7\)

1. Combine like terms on the left side:
\[
5 - 12 + x = x - 7
\]
This simplifies to:
\[
-7 + x = x - 7
\]

2. Next, subtract \(x\) from both sides:
\[
-7 + x - x = x - x - 7
\]
This simplifies to:
\[
-7 = -7
\]

Since both sides of the equation are equal, it shows that the equation is true for all values of \(x\). Therefore, the solution to the equation \(5 + x - 12 = x - 7\) can be stated as:

**Solution:** The equation is true for all real numbers \(x\).

---

### Part B: Verify the solution using \(x = -4\), \(x = 0\), and \(x = 5\)

To verify if these values satisfy the equation \(5 + x - 12 = x - 7\), we will substitute each value into the original equation.

1. **For \( x = -4 \):**
\[
5 + (-4) - 12 \stackrel{?}{=} -4 - 7
\]
Calculate the left side:
\[
5 - 4 - 12 = 1 - 12 = -11
\]
Calculate the right side:
\[
-4 - 7 = -11
\]
The left side equals the right side, so \(x = -4\) is a solution.

2. **For \( x = 0 \):**
\[
5 + 0 - 12 \stackrel{?}{=} 0 - 7
\]
Calculate the left side:
\[
5 - 12 = -7
\]
Calculate the right side:
\[
0 - 7 = -7
\]
The left side equals the right side, so \(x = 0\) is a solution.

3. **For \( x = 5 \):**
\[
5 + 5 - 12 \stackrel{?}{=} 5 - 7
\]
Calculate the left side:
\[
5 + 5 - 12 = 10 - 12 = -2
\]
Calculate the right side:
\[
5 - 7 = -2
\]
The left side equals the right side, so \(x = 5\) is also a solution.

### Summary of Verification:
- For \(x = -4\), both sides equal \(-11\).
- For \(x = 0\), both sides equal \(-7\).
- For \(x = 5\), both sides equal \(-2\).

**Conclusion:** All tested values \(x = -4\), \(x = 0\), and \(x = 5\) verify that the equation \(5 + x - 12 = x - 7\) holds true, confirming that the equation is valid for all real \(x\).

Answer 2

can you use less words and make it less advanced

Answer 3

Sure! Let’s simplify the response:

### Part A: Solve the equation \(5 + x - 12 = x - 7\)

1. Combine like terms on the left:
\[
5 - 12 + x = x - 7
\]
This simplifies to:
\[
-7 + x = x - 7
\]

2. Subtract \(x\) from both sides:
\[
-7 = -7
\]

Since both sides are equal, the equation is true for all values of \(x\).

**Solution:** The equation is true for all real numbers \(x\).

---

### Part B: Check the solution for \(x = -4\), \(x = 0\), and \(x = 5\)

1. **For \(x = -4\)**:
\[
5 + (-4) - 12 \quad \text{and} \quad -4 - 7
\]
Left side: \(5 - 4 - 12 = -11\)

Right side: \(-4 - 7 = -11\)

Both sides equal \(-11\). ✓

2. **For \(x = 0\)**:
\[
5 + 0 - 12 \quad \text{and} \quad 0 - 7
\]
Left side: \(5 - 12 = -7\)

Right side: \(0 - 7 = -7\)

Both sides equal \(-7\). ✓

3. **For \(x = 5\)**:
\[
5 + 5 - 12 \quad \text{and} \quad 5 - 7
\]
Left side: \(5 + 5 - 12 = -2\)

Right side: \(5 - 7 = -2\)

Both sides equal \(-2\). ✓

### Conclusion:
All values \(x = -4\), \(x = 0\), and \(x = 5\) work in the equation. The equation is true for any \(x\).