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

1 Answer
Mar 16, 2017

Answer:

#2 < a <8#

Explanation:

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

#-a < x < a#

This is used in the question here.

#rArr-3 < a-5 < 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.

enter image source here