Question

hayden solved this equation using the steps shown. |x-3|=4. step 1: x-3=4.step 2: x-3+3=4+3. solution: x=7. based on the definition of absolute value, what additional step should hayden do to determine the complete solution to the equation?

Answer 1

step 3: x - 3 = -4

step 4: x - 3 + 3 = -4 + 3

second solution: x = -1

Explanation:

The definition of absolute value is:

|x| = y -> x = y or x = -y

Hayden did only the first part:

|x-3|=4 -> x-3 = 4

And he found the first solution: x = 7.

But know he needs to do the second part, that is, make the right side equal the negative of the left side:

step 3: x - 3 = -4

step 4: x - 3 + 3 = -4 + 3

second solution: x = -1