Solving Absolute Value Equations

zee-f · 2011-05-12 23:08:38

Which equation is represented by the number line?

A|x| = -4
B|x 3| = -4
C|x - 3| = 4
D|x 3| = 0
E|x| = -1

Last edited by zee-f (2011-05-12 23:12:55)

Bob · 2011-05-12 23:33:06

hi zee-f

OK. The number line has 'filled-in' spots at -1 and + 7.

So that means x = -1 or + 7.

So let's look at the possible answers

A|x| = -4

Never this! Because the absolute value means the left hand side is always positive => it cannot be minus anything.

B|x 3| = -4

Same here.

D|x 3| = 0

This is posible but doesn't lead to our value .... only x = 3 fits here.

E|x| = -1

Same as A and B here.

So the only possible contender is

C|x - 3| = 4

But let's check it out thoroughly.

What I like to do with absolute values is to draw a graph ignoring the absolute bit first

that means the line y = x - 3 (see graph below)

Then take the bit of the line where y is negative and flip it up in the x axis so you've made it positive.

That V shaped bit is now the graph of y = |x-3|

So draw a line across at y = +4

Where it intersects gives the solutions .... in this case red arrows point you to x = -1 and x = + 7.

So answer C is the one!

Hope that's is all clear.

Bob

ps I can show you an algebraic way if you want; post back for this.

Last edited by Bob (2011-05-12 23:42:14)

zee-f · 2011-05-12 23:36:38

thank you soooooo much ive been searching every where for the explanation for this thanx yup its all clear

Bob · 2011-05-12 23:43:29

You are very welcome.

Bob

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