Question

How many solutions does the equation |x + 6| − 4 = c have if c = 5? If c = −10? Complete the explanation

Answer 1

For c = 5 → two solutions

For c = -10 → no solutions

Explanation:

We know

`|a|\geq0`

for any real value of a.

|a| = b > 0 - two solutions: a = b or a = -b

|a| = 0 - one solution: a = 0

|a| = b < 0 - no solution

|x + 6| - 4 = c

for c = 5:

|x + 6| - 4 = 5 add 4 to both sides

|x + 6| = 9 > 0 TWO SOLUTIONS

for c = -10

|x + 6| - 4 = -10 add 4 to both sides

|x + 6| = -6 < 0 NO SOLUTIONS

Calculate the solutions for c = 5:

|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9 subtract 6 from both sides

x = 3 or x = -15