Question

Error Analysis: Find, describe & correct the error that a student has made while solving the equation: LaTeX: 4=-2\left(x-3\right)4 = − 2 ( x − 3 ) Step Number Equation 1 LaTeX: 4=-2\left(x-3\right)4 = − 2 ( x − 3 ) 2 LaTeX: 4=-2x-64 = − 2 x − 6 3 LaTeX: 4+6\:=\:-2x\:-\:6\:+\:64 + 6 = − 2 x − 6 + 6 4 LaTeX: 10\:=\:-2x10 = − 2 x 5 LaTeX: \frac{10}{-2}=-\frac{2x}{-2}10 − 2 = − 2 x − 2 6 LaTeX: -5=x

Answer 1

Given:

$4=-2\left(x-3\right)$

To find:

The error that a student has made while solving the equation.

Solution:

We have,

$4=-2\left(x-3\right)$

Using distributive property, we get

$4=-2(x)-2(-3)$

$4=-2x+6$

Subtract 6 from both sides.

$4-6=-2x+6-6$

$-2=-2x$

Divide both sides by -2.

$1=x$

The value of x is 1.

In step 2, the distributive property is not used properly because when -2 is distributive with -3 then we get 6 instead of -6.

Therefore, the student has made error in step 2.