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

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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

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

Dec 7, 2017