Question

Graph the following expression on the number line by placing the dot in the proper location. |2 - x | = 4

Answer 1

Plot two points. One point is at -2. The other point is at 6.

Explanation:

The rule we'll use is

if |y| = k, then y = k or y = -k

where k is some positive number.

In this case, y = 2-x and k = 4

So we go from

|2-x| = 4

to these two equations

2-x = 4 or 2-x = -4

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From here we solve each equation for x

2-x = 4

2-x+x = 4+x

2 = 4+x

4+x = 2

x+4 = 2

x+4-4 = 2-4

x = -2 which is one solution

and

2-x = -4

2-x+x = -4+x

2 = -4+x

-4+x = 2

x-4 = 2

x-4+4 = 2+4

x = 6 is the other solution