Question

Part A: Solve the equation 5 + (-12) = 2z - 7. In your final answer, be sure to state the solution and include all your work.

Part B: Use the values z = -0.5, z = 0, and z = 1 to prove your solution to the equation 5 + z - 12 = 2z - 7. In your final answer, include all of your calculations.

Answer 1

The equation 5 + (-12) = 2z - 7 simplifies to -7 = 2z - 7; adding 7 to both sides yields z = 0. Substitution of the values z = -0.5, z = 0, and z = 1 into the original equation confirms that the correct solution is z = 0.

Step-by-step explanation:

Solving the Equation 5 + (-12) = 2z - 7

To solve the equation 5 + (-12) = 2z - 7, we simplify both sides of the equation. The left side simplifies to -7. The equation then becomes:

-7 = 2z - 7

We then add 7 to both sides to isolate the variable term:

0 = 2z

Dividing both sides by 2 yields:

z = 0

Proving the Solution

We will now prove the solution using the values z = -0.5, z = 0, and z = 1 and substitute them into the equation 5 + z - 12 = 2z - 7:

The calculations confirm that the correct solution to the equation is z = 0.