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1. What is the solution to the compound inequality in interval notation?

2(x + 3) > 6  or  2x + 3 ≤ −7

 

A. (−∞, 0)   or  [5, ∞)

B. (−∞, −5] or (2, ∞)

C. (−∞, −2] or  (0, ∞)

D. (−∞, −5] or (0, ∞)

 

2. Matt is five years older than twice his cousin Andy’s age. The sum of their ages is less than 35.

Let x represent Andy's age.

Which inequality represents Andy’s possible age?

 

A.0 < x < 25

B.0 < x ≤10

C.0 < x < 10

D.0 < x ≤ 25

 
AngelRay  Dec 7, 2017
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2(x + 3) > 6  or  2x + 3 ≤ −7       "or"  means  "union"....so we have

 

2x + 6 >  6       or      2x + 3 ≤ -7

2x > 0              or      2x  ≤ -10

x> 0                 or        x ≤ -5

 

This says that  

 

( - inf, -5 ]  or (0, inf)   ⇒   D

 

 

 

Let Andy's age  = x

Then Matt's age  is   twice Andy's age + 5  =  2x + 5

 

And we know that  

 

x + 2x + 5  <  35     simplify

 

3x + 5  < 35

 

3x  <  30

 

x < 10

 

So we have that       0 < x < 10    ⇒    C

 

 

cool cool cool

 
CPhill  Dec 7, 2017

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