Question

Write the absolute value equations in form lx-bl=c that have the following solution sets-
two solutions: x=2; x=14

Answer 1

Step-by-step explanation:

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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