Question 996719
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