+912 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
+128407 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
