SOLUTION: Solve the following compound inequality and write down the solution in interval notation: 2x – 4 < 0 or 6 – x < 3

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Question 147213: Solve the following compound inequality and write down the solution in interval notation: 2x – 4 < 0 or 6 – x < 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's solve the first inequality 2x-4%3C0:


2x-4%3C0 Start with the first inequality.


2x%3C0%2B4 Add 4 to both sides.


2x%3C4 Combine like terms on the right side.


x%3C%284%29%2F%282%29 Divide both sides by 2 to isolate x.


x%3C2 Reduce.


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Now let's solve the second inequality 6-x%3C3:


6-x%3C3 Start with the second inequality.


-x%3C3-6 Subtract 6 from both sides.


-x%3C-3 Combine like terms on the right side.


x%3E%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E3 Reduce.


So our answer is x%3C2 or x%3E3



So the solution in interval notation is: () ()