MAT-142 Precalculus With Limits (Southern New Hampshire University – Module 1 Problem Set) – Fully Worked Solutions

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MAT-142-X2573 Precalculus with Limits 23EW2 : MAT-142 : 1421222, 1-4 Module One Problem Set
Tracey Delton, 10/27/23 at 1:01:22 PM EDT
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Question1: Score 2/2

Solve the compound inequality: 6 ≤ 2 x − 8 < 12 .
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Enter the exact answer in interval notation.
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To enter ∞ , type infinity. To enter ∪ , type U.
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Your response Correct response
[7,10) [7, 10)
Auto graded Grade: 1/1.0 
N
KS
 Total grade: 1.0×1/1 = 100%
Feedback:

Write two separate inequalities: 6 ≤ 2 x − 8 and 2 x − 8 < 12 . We solve them independently.
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6 ≤ 2 x − 8 and 2x − 8 < 12
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14 ≤ 2 x 2x < 20



7 ≤ x x < 10
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Therefore, the solution set is 7 ≤ x < 10 , or in interval notation, [7, 10).
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Question2: Score 1.6/8
N
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, Solve the inequality involving absolute value.
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|x − 3| + 5 ≥ 12




Enter the exact answer in interval notation.
S

To enter ∞ , type infinity. To enter ∪ , type U.
TB

Your response Correct response
(-infinity,-4]U[10,infinity) (-infinity, -4] U [10, infinity)
Auto graded Grade: 25/25.0 
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Show your work and explain, in your own words, how you arrived at your answers.
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|x-3| + 5 >= 12
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|x-3| + 5 - 5 >= 12 - 5
|x - 3| >= 7
Case 1:
x - 3 >= 7
x >= 7 + 3
x >= 10
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Case 2:
-( x - 3) >= 7
-x + 3 >= 7
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-x >=4
x <=-4
(-infinity,-4]U[10,infinity)

Ungraded Grade: 0/100.0
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 Total grade: 1.0×25/125 + 0.0×100/125 = 20% + 0%
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Question3: Score 2/2
N
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, Solve the inequality involving absolute value.


∣ x−3 ∣
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< 3
∣ 5 ∣




Enter the exact answer in interval notation.
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To enter ∞ , type infinity. To enter ∪ , type U.
TB

Your response Correct response
(-12,18) (-12, 18)
Auto graded Grade: 1/1.0 
A

 Total grade: 1.0×1/1 = 100%
N
Feedback:

∣ x−3 ∣
< 3
∣ 5 ∣
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x−3
−3 < < 3
5


−15 < x − 3 < 15
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−12 < x < 18
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Express the inequality in interval notation.
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(−12, 18)
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Question4: Score 2/2
N
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