Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution sets:
A.Two solutions: x=2, x=13.
B.One solution: x=23.
C.Two solutions: x= 1/2 , x=− 1/3 .
D.One solution: x=−3.
E.One solution: x=−4.1.
F.All numbers such that x≥5.
G.All numbers such that x≤5.
H.All numbers such that x≤−14.
I.All numbers such that x≥−1.3.
Answers
Given : equations in the form x−b=c and solution sets
To find : Find expression / equation
Solution:
x−b=c
2 - b = c
13 - b = c
only possible
if | 2 - b| = | 13 - b|
=> 13 - b = b - 2
=> 2b = 11
=> b = 11/2
x - 11/2 = √25
x=23
=> x + 2 = 25
1/2 - b = b + 1/3
=> 2b = 1/6
=> b = 1/12
x - 1/12 = √(25/144)
x = - 3
=> x + 3 = 0
x=−4.1.
=> x + 4.1 = 0
All numbers such that x≥5.
x - 5 ≥ 0
All numbers such that x≤5.
x - 5 ≤ 0
All numbers such that x≤−14.
=> x + 14 ≤ 0
All numbers such that x≥−1.3.
=> x + 13 ≥ 0
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Answer: a=|x+17|=15
Step-by-step explanation: