Kendra F. answered • 02/02/17
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lxl +5 > 11
split into two inequalities (±x)
x + 5 > 11
-5
x > 6
-x + 5 > 11
-5 both sides
-x > 6
divide by -1, reverses inequality sign
x < -6
Kendra F.
I made the x both positive and negative because it's an absolute value inequality. |±x| = positive x. To remove the absolute value bracket you need to solve it as both ± signs.
can also be done like so;
|x| + 5 > 11
-5 both sides
|x| > 6
remove absolute value brackets by showing it can be both ± numbers, inequalities face same direction
-6 > x > 6
* note - do this when you only have an absolute value left on one side, must first -5
Another example
|2x + 3| < 6
starting with only an absolute value on one side so you can remove brackets like so
-6 < 2x + 3 < 6
inequalities are facing same direction, solve using algebra
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02/02/17
Chris C.
I thought you were suppose to change the value outside of the absolute value.
l2xl >4 or l2xl >-4
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02/02/17
Kendra F.
You can either change the values outside and add the second inequality or solve for both ±x
Since its an absolute value inequality, for |2x|>4
you must solve both 2x > 4 and 2x < -4
best to write it like this
-4 > 2x > 4
so you know which direction the inequality signs face
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02/02/17
Chris C.
02/02/17