SOLUTION: |6-4x|>2
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Algebra: Inequalities, trichotomy
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Question 177246
:
|6-4x|>2
Answer by
jim_thompson5910(35256)
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Start with the given inequality
Break up the absolute value (remember, if you have
, then
or
)
or
Break up the absolute value inequality using the given rule
Now lets focus on the first inequality
Start with the given inequality
Subtract 6 from both sides
Combine like terms on the right side
Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)
Divide
Now lets focus on the second inequality
Start with the given inequality
Subtract 6 from both sides
Combine like terms on the right side
Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)
Divide
----------------------------------------------------
Answer:
So our answer is
or
which looks like this in interval notation
if you wanted to graph the solution set on a number line, you would get:
Graph of the solution set in blue and the excluded values represented by open circles