Question

3. Error Analysis Isabel says that the equation x - 2 = -(x - 2) has no
solution because a number can never be equal to its opposite. Explain the
error Isabel made

Answer 1

Given:

The equation is

$(x-2)=-(x-2)$

Isabel says that the given equation has no  solution because a number can never be equal to its opposite.

To find:

Isabel's mistake.

Solution:

Her reason "a number can never be equal to its opposite" is not correct.

Zero is a number that can be equal to its opposite.

So, the given equation has solution for which LHS=RHS=0.

We have,

$(x-2)=-(x-2)$

$x-2=-(x)-(-2)$

$x-2=-x+2$

Add x and 2 on both sides.

$x-2+x+2=-x+2+x+2$

$2x=4$

Divide both sides by 2.

$x=\dfrac{4}{2}$

$x=2$

So, the given equation has a solution x=2.