Question

1. describe and correct the error in solving the equation.

x
0.4x = 0.2(x - 8)
0.4x = 0.2x - 8
0.2x = -8
x = -4

Explanation:

Step1: Identify the error

When distributing \(0.2\) to \((x - 8)\), the correct calculation should be \(0.2\times x-0.2\times8 = 0.2x - 1.6\), not \(0.2x - 8\). So the error is in the distribution step.

Step2: Correct the distribution

Start with the original equation: \(0.4x=0.2(x - 8)\)
Distribute \(0.2\) properly: \(0.4x = 0.2x-0.2\times8\)
Simplify the right - hand side: \(0.4x=0.2x - 1.6\)

Step3: Solve for \(x\)

Subtract \(0.2x\) from both sides: \(0.4x-0.2x=0.2x - 1.6-0.2x\)
Simplify both sides: \(0.2x=-1.6\)
Divide both sides by \(0.2\): \(x=\frac{-1.6}{0.2}=-8\)

Answer:

The error was in the distribution of \(0.2\) to \((x - 8)\) (it should be \(0.2x-1.6\) not \(0.2x - 8\)). The correct solution is \(x=-8\).