How do you solve equations and inequalities using absolute values?
Equation: [ x - 3] = 5
Inequality: [3y - 2 ] > 7 *the carrot should have a line under it representing greater or equal to
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
-(x - 3) = 5 because the absolute value makes it positive automatically.
So, for the first part
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.
Any time ;)
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