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

Question

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 \(x\).

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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 \(x\).

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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 \(x\).