CAHSEE Math 1.5 Algebra I. Find the solution to the absolute value inequality.
|Algebra I||Solving absolute values|
|CAHSEE Math||Algebra I|
|Functions||Absolute Value Functions|
We have to put numbers on either side of our variable… so we have a range for x.
We really have 2 equations we’re solving here as with any absolute value problem…
and we start with the rosy, positive one.
First assume that the absolute value things don’t exist… and it’s just the quantity
x minus 3 is less than 7.
So we add 3 to both sides to get x is less than 10. We know 10 is on the end… and we
can cross out A or B as potential answers.
But now let’s think about how we solve for the LESS THAN part of the equation.
We need to flip the little “greater than” thingy here – how do we do that?
We multiply by a negative number – in this case… negative 1.
So think about it as negative 1 times the quantity x minus 3… all now GREATER than 7.
We get negative x plus 3 is greater than 7…
Subtract 3 from both sides to get negative x is greater than 4…
…then divide both sides by negative one to get x is greater than negative 4…
So our answer is C.
As in, “Claustrophobia.”