Given the equation 5 + x -14 = x-7

Question

Part A. Solve the equation 5 + x -14 = x-7
. In your final answer, be sure to state the solution and include all of your work.

Part B. Use the values 2, 0, 3
to verify your solution to the equation 5 + x -14 = x-7
. In your final answer, include all of your calculations.

Answer 1

Let's solve the equation step by step for Part A.

Part A: Solve the equation \( 5 + x - 14 = x - 7 \)

1. Simplify the left side: \[ 5 + x - 14 = x - 7 \] Combine \(5\) and \(-14\): \[ -9 + x = x - 7 \]

2. Eliminate \(x\) from both sides: Subtract \(x\) from both sides: \[ -9 = -7 \]

3. Analyze the result: The equation \(-9 = -7\) is a false statement, indicating that there are no values for \(x\) that satisfy this equation.

Therefore, there is no solution to the equation \(5 + x - 14 = x - 7\).

Final answer for Part A: No solution.

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Part B: Verify the solution using the values \(2\), \(0\), and \(3\)

Since we concluded in Part A that there is no solution, we can substitute the values of \(2\), \(0\), and \(3\) into the original equation to confirm that they indeed do not satisfy the equation.

1. Substituting \(x = 2\): \[ 5 + 2 - 14 = 2 - 7 \] Calculate the left side: \[ 5 + 2 - 14 = -7 \] Calculate the right side: \[ 2 - 7 = -5 \] Since \(-7 \neq -5\), \(x = 2\) does not satisfy the equation.

2. Substituting \(x = 0\): \[ 5 + 0 - 14 = 0 - 7 \] Calculate the left side: \[ 5 - 14 = -9 \] Calculate the right side: \[ 0 - 7 = -7 \] Since \(-9 \neq -7\), \(x = 0\) does not satisfy the equation.

3. Substituting \(x = 3\): \[ 5 + 3 - 14 = 3 - 7 \] Calculate the left side: \[ 5 + 3 - 14 = -6 \] Calculate the right side: \[ 3 - 7 = -4 \] Since \(-6 \neq -4\), \(x = 3\) does not satisfy the equation.

Final answer for Part B: All the tested values (\(2\), \(0\), and \(3\)) do not satisfy the equation \(5 + x - 14 = x - 7\), confirming that there is no solution.

Answer 2

can you use less words and make it less advanced

Answer 3

Sure! Let's simplify the explanation.

Part A: Solve the equation \(5 + x - 14 = x - 7\)

1. Start with the equation: \[ 5 + x - 14 = x - 7 \]

2. Combine \(5\) and \(-14\) on the left: \[ -9 + x = x - 7 \]

3. Subtract \(x\) from both sides: \[ -9 = -7 \]

Since \(-9\) does not equal \(-7\), there is no solution.

Final answer for Part A: No solution.

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Part B: Verify with values \(2\), \(0\), and \(3\)

1. For \(x = 2\): \[ 5 + 2 - 14 = 2 - 7 \] Left side: \(5 + 2 - 14 = -7\)
   Right side: \(2 - 7 = -5\)
   They are not equal.

2. For \(x = 0\): \[ 5 + 0 - 14 = 0 - 7 \] Left side: \(5 - 14 = -9\)
   Right side: \(0 - 7 = -7\)
   They are not equal.

3. For \(x = 3\): \[ 5 + 3 - 14 = 3 - 7 \] Left side: \(5 + 3 - 14 = -6\)
   Right side: \(3 - 7 = -4\)
   They are not equal.

Final answer for Part B: None of the values \(2\), \(0\), or \(3\) work, confirming that there is no solution.