SOLUTION: 19) Solve <pre> 4x-7 <-5 or 4x-7 > 2 8 8 </pre>

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Question 146070: 19) Solve

        4x-7 <-5 or 4x-7  > 2
         8            8

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve %284x-7%29%2F8%3C=-5


%284x-7%29%2F8%3C=-5 Start with the first inequality.


4x-7%3C=8%28-5%29 Multiply both sides by 8.


4x-7%3C=-40 Multiply.


4x%3C=-40%2B7 Add 7 to both sides.


4x%3C=-33 Combine like terms on the right side.


x%3C=%28-33%29%2F%284%29 Divide both sides by 4 to isolate x.


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Answer:

So our first answer is x%3C=-33%2F4


Which approximates to x%3C=-8.25





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Now let's solve %284x-7%29%2F8%3E=2


%284x-7%29%2F8%3E=2 Start with the given inequality.


4x-7%3E=8%282%29 Multiply both sides by 8.


4x-7%3E=16 Distribute and multiply.


4x%3E=16%2B7 Add 7 to both sides.


4x%3E=23 Combine like terms on the right side.


x%3E=%2823%29%2F%284%29 Divide both sides by 4 to isolate x.


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Answer:

So our second answer is x%3E=23%2F4


Which approximates to x%3E=5.75





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So the final answer is

x%3C=-33%2F4 OR x%3E=23%2F4


which is approximately


x%3C=-8.25 OR x%3E=5.75