ACT Math Intermediate Algebra: Drill 2, Problem 4. Solve for x.
|ACT Math||Intermediate Algebra|
|ACT Mathematics||Intermediate Algebra|
|Foreign Language||Arabic Subtitled|
|Intermediate Algebra||Absolute value equations and inequalities|
Inequalities and absolute value equations
|One-Variable Equations and Inequalities||Solving Inequalities|
|Product Type||ACT Math|
It's a pretty vanilla absolute value question.
We can ignore the vertical lines for a moment...so we have 4x plus 2 minus 3 is greater than
or equal to 15... or 4x minus 1 is greater than or equal to 15.
Then... 4x is greater than or equal to 16... so x is greater than or equal to 4.
Again, that's only if we ignore the absolute value lines.
So now let's max out what we can do if we color... inside the lines.
We're going to worry about the absolute value of 4x plus 2 being greater than or equal to 18...
...so... think about what x value could make 4x plus 2 NEGATIVE 18; we'll then take the
absolute value of that to make it GREATER than 18.
That is, what NEGATIVE values of x would do this for us?
Well, negative 1, 2 and 3 and 4 don't help us much, but negative 5 gets us there because
we have 4 times negative 5, which is negative 20...
... then add 2, and we have negative 18, but when we take the absolute value of it we're there.
So the range that x can take to satisfy this equation is that it lives somewhere between
negative 5 and positive 4...
And that's why you always have to be careful to... stay inside the lines.