Question

Write an absolute value equation to satisfy the given solution set shown on a number line.

Answer 1

Answer:

|x + 6|  = 2

Step-by-step explanation:

For a general absolute value equation:

| f(x) |  = b

We can rewrite it as:

f(x) = b

f(x) = -b

with b > 0.

Because in the number line we have only two points graphed, this means that our absolute value equation has two solutions.

And we can conclude that one solution comes from the equation:

f(x) = b

And the other solution comes from the equation:

f(x) = -b

And thus, f(x) is a linear equation, that we can simply write as:

x - c

Then our equations can be rewritten as:

x - c = b

x -c = -b

Now let's look at the graph, we can see that the two solutions are:

x = -8

and

x = -4

Let's input each one of these in one of our above equations (the order does not matter).

-4 - c = b

-8 - c = -b

The larger value of x, (x = -4) needs to be in the equation with the positive value of b.

From the first equation we can get:

b = -4 - c

now we can replace the variable "b" in the second equation by "-4 - c" to get:

-8 - c = -(-4 - c)

-8 - c = 4 + c

-8 - 4 = c + c

-12 = 2c

-12/2  =c

-6 = c

Now that we know the value of c, we can input it in the equation:

b = -4 - c

to find the value of b

b = -4 - (-6) = -4 + 6 = 2

b = 2

Then the absolute value equation is:

|x - (-6) | = 2

|x + 6|  = 2