Question

Can you help me with this!!

|x+3|= -7

Answer 1

|x+3|= -7
-3 -3
X= -10
X/1 those cancel out
-10/1
So x= -10 that’s the first answer

Second answer is
-|x+3|= -7
Multiply everything by -1
-1x+3= -7
-3 -3
-1x = -10
-1x/ -1 those cancel out
-10/-1
X= 10 that’s ur second answer
Hope that helps <3

Answer 2

For any absolute value question: either x+3 is positive, and
`|x+3|=x+3`, or x+3 is negative, and
`|x+3|=-(x+3)` (so that the output will be positive)

This gives us two options. First, we do the case for if x + 3 is positive, then we solve the case if x + 3 is negative. If both work, we get two answers to the equation.

But, this only works if our initial assumptions are even possible. Absolute value is always positive, but in this equation we have to equal to a negative number. This isn't possible, so there is no solution.

Even in an equation where this isn't the case, it's important to check that your initial assumption was even possible by plugging in x and making sure it's positive or negative. If it isn't, you have an extraneous solution - a value that isn't actually a solution.