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Chapter 6: Problem 44

Solve and check each equation. \(-2(z-4)-(3 z-2)=-2-(6 z-2)\)

Short Answer

Expert verified
The solution for the equation is \( z = -10 \)

Step by step solution

01

Simplify the equation

First distribute the negatives through the parentheses to get the equation down to an easier form to work with. This results in: \n\(-2z + 8 - 3z + 2 = -2 - 6z + 2\)
02

Group like terms

Combine like terms on both sides of the equation: \n\(-5z + 10 = -6z \)
03

Move variables to one side

Next move the variable term to one side of the equation only. This is done by adding \( 6z \) to both sides to remove it from the right side of the equation: \n\(z + 10 = 0\)
04

Isolate the variable

Finally, isolate \( z \) by subtracting 10 from both sides of the equation to leave \( z \) on its own: \n\(z = -10\)
05

Check the solution

To ensure the solution is correct, substitute \( z = -10 \) back into the original equation and check each side. If the equality holds true for the equation, then the solution is correct.

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