Math 137 Online Week 1 Outline and Practice Problems
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Math 137 Online
Week 1 Outline and Practice Problems
Practice Problems
Each week there will be practice problems posted, along with a “Practice Quiz” meant to be practice for the kinds of questions that appear on your Mobius assessments.
1. Solve the following equations/inequalities
(a) Ix - 2I = 5
(b) Ix - 4I = I3x + 2I
(c) 1 < Ix + 1I
(d) Ix + 3I + I1 - 2xI < 5 (e) Ix - 4IIx + 2I > 7
2. Prove that, for any real numbers a and b
(a) IaI - IbI < Ia + bI
(b) IaI - IbI < Ia - bI
Hint: Consider using the triangle inequality.
3. Write the expression
(a + b + Ia - bI)
as a piecewise function. You should consider 2 cases. What is this expression essentially calculating for any two real numbers a and b?
Practice Quiz
1. Which of the following statements are true (select all that apply):
(a) Ix + yI 2 IxI + IyI for all x, y e R
(b) IIxI - IyII < Ix - yI for all x, y e R
(c) If 0 < x2 < 2 then 0 < x < ,2
(d) If IxI = 2 then 3x + 2 2 4 + 2x
(e) If 0 < a < b then 
< 
(f) None of the above.
2. What values of x will satisfy the inequality π < Ix - 1I < 5 (select all that apply):
(a) x e [-3, -2] u [2, 3]
(b) x e [-4, π + 1)
(c) x e [-4, -π + 1) u (π + 1, 6]
(d) x e [-4, -π + 1] u (π + 1, 6]\{-π + 1}
(e) x e (-π + 1, π + 1)
(f) x e [5, 6]
(g) None of the above.
2023-02-11