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Question 996719: Write an absolute value equation representing the following; then solve the equation.
Numbers that are 7 units from -3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! these can be tricky to figure out.
you are basically looking for 2 values of x.
first x will be to the left of -3.
second x will be to the right of -3.
both x's will be 7 units away from -3.
if you do this correctly, you will find that x to the left is equal to -10 and x to the right is equal to 4.
you can develop the absolute value equation as follows:
x = -3 - 7
or
x = -3 + 7
add 3 to both sides of each equaiton to get:
x+3 = 7
x+3 = -7
this fits the basic definition of an abslute value equation that states:
if |x| = y, then x = y or x = -y
x in this definition represents any expression enclosed within the absolute value signs.
from this, you can derive your absolute value equation that states:
|x+3| = 7
by the basic definition, this means that:
x+3 = 7 or x+3 = -7
from those equations, you get x = 4 or x = -10.
-10 is 7 units away from -3.
4 is 7 units away from -3.
your solution is:
|x+3| = 7
x = -10 or x = 4
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