Question

here is how zee solved an equation.
circle the mistake and explain why zees work is wrong.
zee
-2(3x - 5) = 4(x + 3) + 8
-6x + 10 = 4x + 12 + 8
-6x + 10 = 4x + 20
10 = -2x + 20
-10 = -2x
5 = x
what is the correct solution?

Explanation:

Step1: Analyze the step of moving terms

When moving \(4x\) from the right - hand side to the left - hand side, the sign should change. Zee made a mistake here. The correct operation is:
Starting from \(-6x + 10=4x + 20\), we should get \(10=4x + 6x+20\) (by adding \(6x\) to both sides), not \(10=-2x + 20\).

Step2: Solve the correct equation

Starting from the correct expansion \(-6x + 10 = 4x+12 + 8\) (which simplifies to \(-6x + 10 = 4x + 20\)):
Add \(6x\) to both sides of the equation:
\(-6x+6x + 10=4x+6x + 20\), which gives \(10 = 10x+20\).
Subtract \(20\) from both sides: \(10-20=10x+20 - 20\), so \(-10 = 10x\).
Divide both sides by \(10\): \(x=\frac{-10}{10}=-1\).

Answer:

Zee's mistake is in the step \(10=-2x + 20\) (the sign change when moving \(4x\) is incorrect). The correct solution is \(x = - 1\).