Equations and Equalities Involving Absolute Values

label Algebra
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How do you solve equations and inequalities using absolute values?

Thanks!

Example:

Equation: [ x - 3] = 5

Inequality: [3y - 2 ] > 7    *the carrot should have a line under it representing greater or equal to 

May 20th, 2015

You must solve for the positive AND negative parts.

In other words, in your example:

[x - 3] = 5   there are TWO equations that are true

x - 3 = 5

AND

-(x - 3) = 5   because the absolute value makes it positive automatically.

So, for the first part

x - 3 = 5

x = 8

and for the second part

-(x - 3) = 5

x - 3 = - 5

x = - 2

So there are TWO answers that satisfy the absolute value equation [x - 3] = 5

Now, let's look at the inequality:

[3y - 2] > 7

Same rule applies:

3y - 2 > 7

3y > 9

y > 3   That takes care of the positive part, now for the negative part

-(3y - 2) > 7

But here's the thing to remember about inequalities. Whenever you multiply or divide by a negative number, it turns the inequality around, so:

3y - 2 < - 7   See that?

Now continue to solve:

3y < - 5

y < -5/3

And that's it! Hope this answers your questions.

May 20th, 2015

Thank you!

May 20th, 2015

Any time ;)

May 20th, 2015

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