ACT Math 2.4 Intermediate Algebra

ACT Math Intermediate Algebra: Drill 2, Problem 4. Solve for x.

ACT MathIntermediate Algebra
ACT MathematicsIntermediate Algebra
Foreign LanguageArabic Subtitled
Chinese Subtitled
Korean Subtitled
Spanish Subtitled
Intermediate AlgebraAbsolute value equations and inequalities
Inequalities and absolute value equations
LanguageEnglish Language
One-Variable Equations and InequalitiesSolving Inequalities
Product TypeACT Math

Transcript

00:20

It's a pretty vanilla absolute value question.

00:24

We can ignore the vertical lines for a moment...so we have 4x plus 2 minus 3 is greater than

00:30

or equal to 15... or 4x minus 1 is greater than or equal to 15.

00:36

Then... 4x is greater than or equal to 16... so x is greater than or equal to 4.

00:44

Again, that's only if we ignore the absolute value lines.

00:49

So now let's max out what we can do if we color... inside the lines.

00:53

We're going to worry about the absolute value of 4x plus 2 being greater than or equal to 18...

01:00

...so... think about what x value could make 4x plus 2 NEGATIVE 18; we'll then take the

01:07

absolute value of that to make it GREATER than 18.

01:10

That is, what NEGATIVE values of x would do this for us?

01:14

Well, negative 1, 2 and 3 and 4 don't help us much, but negative 5 gets us there because

01:20

we have 4 times negative 5, which is negative 20...

01:24

... then add 2, and we have negative 18, but when we take the absolute value of it we're there.

01:35

So the range that x can take to satisfy this equation is that it lives somewhere between

01:39

negative 5 and positive 4...

01:41

...Answer: A.

01:43

And that's why you always have to be careful to... stay inside the lines.