Question

For each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
a)

Answer 1

The expression $|x|-5 = d$, where $x \in [5, 17]$ and $d \in [0,12]$, satisfy the given solution set.

How to apply absolute value properties to define a given solution set

Let be 5 and 17 are the lower and upper bounds of the given interval. Thus, both positive numbers. Based on the information presented by the figure:

$|x-5| = d$, where $x \in [5, 17]$ and $d \in [0,12]$.

$|x|-|5| = d$

$|x|-5 = d$, where $x \in [5, 17]$ and $d \in [0,12]$. (1)

The expression $|x|-5 = d$, where $x \in [5, 17]$ and $d \in [0,12]$, satisfy the given solution set. $\blacksquare$

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Answer 2

Answer:

|y-11|=6

Step-by-step explanation: