Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Solve the equation. Check for extraneous solutions.

9|9−8x|=2x+3

Answer 1

First, we will solve for the positive value inside the absolute value.

9 - 8x = 2x + 3.

We will start solving for x by combining like terms:

9 - 3 = 2x + 8x.

6 = 10x.

Next, we divide both sides by 10 to solve for x:

6/10 = 10x/10,

0.6 = x.

So, x = 0.6 is a potential solution.

Now, we will solve for the negative value inside the absolute value:

-(9 - 8x) = 2x + 3.

We will start solving for x by distributing the negative sign:

-9 + 8x = 2x + 3.

Next, we will combine like terms:

8x - 2x = 3 + 9,

6x = 12.

Dividing both sides by 6:

x = 12/6,

x = 2.

So, x = 2 is another potential solution.

Now, we will check for extraneous solutions by substituting each potential solution back into the original equation:

For x = 0.6:

9|9 - 8(0.6)| = 2(0.6) + 3,

9|9 - 4.8| = 1.2 + 3,

9|4.2| = 4.2 + 3,

9(4.2) = 7.2,

37.8 = 7.2,

This is not true, so x = 0.6 is an extraneous solution and is not a solution to the equation.

For x = 2:

9|9 - 8(2)| = 2(2) + 3,

9|9 - 16| = 4 + 3,

9|-7| = 7,

9(7) = 7,

63 = 7,

This is not true, so x = 2 is an extraneous solution and is not a solution to the equation.

Therefore, the equation has no real solutions.