How do you solve and graph abs(a-5)<3|a5|<3?

1 Answer
Mar 16, 2017

2 < a <82<a<8

Explanation:

The standard form for |x| < a |x|<a is.

-a < x < aa<x<a

This is used in the question here.

rArr-3 < a-5 < 33<a5<3

Isolate a in the centre interval by adding 5 to ALL 3 intervals.

rArr-3+5 < acancel(-5)cancel(+5) < 3+5

rArr2 < a < 8larr" is the solution"

To show the solution on a number line place color(blue)"open circles" at 2 and 8 to indicate that 2 and 8 are not values in the solution. If they were we use a solid circle to denote they are part of the solution.

The solution is the values color(blue)"between" 2 and 8 which is denoted by a heavy line drawn between the 2 open circles.

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