The inequalities (1/5)x + 7 ≤ 11 and (–1/5)x – 7 ≥ –11 have the same solutions. What are the solutions for both inequalities? Explain your reasoning. *
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Answer:
Both of the given equations have same solution.
Step-by-step explanation:
According to the properties of inequalities :
- Suppose if x > a, then on multiplying or dividing both sides by - 1 , - x < - a
On this basis it can said that (1/5)x + 7 ≤ 11 will be same when multiplied by - 1 .
It says :
= > (1/5)x + 7 ≤ 11
= > (-1){ (1/5)x + 7 } ≤ (-1)11
= > (-1/5)x - 7 ≥ - 11
However, if one is unaware of this property :
= > (1/5)x + 7 ≤ 11
= > (1/5)x + 7 - [ (1/5)x + 7 ] ≤ 11 - [ (1/5)x + 7 ]
= > 0 ≤ 11 - [ (1/5)x + 7 ]
= > - 11 ≤ 11 - 11 - [ (1/5)x + 7 ]
= > - 11 ≤ (-1/5)x - 7
And therefore both of the equations have same solution.
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