Question

How many solutions does the following absolute value equation have? |x+3|=4

Answer 1

The absolute value equation |x+3|=4 has two solutions: x = 1 and x = -7.

Step-by-step explanation:

To solve the absolute value equation |x+3|=4,

We need to consider two cases:

Case 1: (x+3) = 4

Solving this equation, we get:

x+3 = 4

x = 4 - 3

x = 1

Case 2: -(x+3) = 4

Solving this equation, we get:

-x-3 = 4

-x = 4 + 3

-x = 7

Multiplying both sides by -1, we get:

x = -7

So, the absolute value equation |x+3|=4 has two solutions: x = 1 and x = -7.