Question

HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
x−c=d, where c and d are some numbers, to satisfy the given solution set.

x= -8, and x= -4

Answer 1

Answer:

$|x + 6| = 2$

Step-by-step explanation:

We want to write an absolute value equation in the form:

$|x - c| = d$

where c and d are some numbers, to satisfy the given solution set

x= -8, and x= -4

We apply the definition of absolute value to get:

$x - c = d \: or \: x - c = - d$

This implies that;

$x = c + d \: or \: x = c- d$

By comparing to

x=-8 or x=-4

We have:

$c + d = - 4 \\ and \\ c - d = - 8$

Add both equations to eliminate d:

$2c = - 12$

$c = - 6$

This implies that;

$d = - 4 - - 6 = 2$

The required absolute value equation is:

$|x + 6| = 2$