what is |4a-2|=10 etc.?

Question

Solve each equation or inequality

1)|4a-2|=10

2)|9-3g|<=12

3)|x-5|> 3

Answer 1

1. For an equals absolute value problem, you simply have two (possible) answers.  Set up the problem for the negative possibility and the positive one:
1. 4a-2=10   OR 4a-2=-10
2. 4a=12      OR 4a=-8
3. a=3          OR a=-2
2. For a less than situation, you will have a (possible) range, that is of the form a<x<b.  Start by setting up your absolute value piece as between the negative and positive number you start with.
1. -12 < 9-3g < 12
2. -21 < -3g < 3
3. 7 > g > -1 (remember multiplying or dividing by a negative number turns things around)
4. -1 < g < 7 (putting it back into the right order)
3.  For a greater than situation, you will have two "tails" so to speak of allowable values.  Start by setting up two distinct problems using the positive and negative starting value
1. x-5<-3    OR   x-5>3
2. x<2       OR  x>8