Question

What is the solution to the equation -6z 1=-4-7z , given the replacement set -5, -3, -1 ?

1) -5
2) -3
3) -1
4) Cannot be determined

Answer 1

After isolating and solving the variable z in the equation -6z + 1 = -4 - 7z, we find that z = -5, which is included in the replacement set provided. Hence, the solution to the equation is z = -5.

Step-by-step explanation:

To solve the equation -6z + 1 = -4 - 7z, we shall first isolate the variable z on one side of the equation. Let's add 7z to both sides to move the z terms to the same side.

-6z + 7z + 1 = -4 - 7z + 7z

This simplifies to:

z + 1 = -4

Next, we subtract 1 from both sides to solve for z:

z = -4 - 1

z = -5

Now we check the replacement set {-5, -3, -1} to see which number is the solution to the equation. As we have determined z is -5, this matches the first number in our replacement set.

Therefore, the solution to the equation is -5.