Solve each equation. Show the solution on a number line

Question

l8-xl=5

Answer 1

To solve for x, we need to isolate it on one side of the equation. Let's subtract 8 from both sides:

l8 - xl = 5
-8 -8

l -xl = -3

Next, we need to get rid of the absolute value bars. We can do this by breaking the equation up into two cases:

Case 1: 8 - x if x ≤ 8
Case 2: x - 8 if x > 8

For case 1, we will substitute 8 - x for the absolute value.

-(8 - x) = -3

Simplify by distributing the negative sign:

-x + 8 = -3

Subtract 8 from both sides:

-x = -11

Finally, divide by -1 to solve for x:

x = 11

For case 2, we will substitute x - 8 for the absolute value.

x - 8 = -3

Add 8 to both sides:

x = 5

So the solution set is {5, 11}, and we can represent this on a number line like this:

<--------------●-----------●------------->
5 11

Answer 2

come on bot, you can do better than that!
Your answer is wrong!!!!
Why didn't you think to see if your answers verify???

l8-xl=5
8-x = 5 or -8+x = 5
-x = -3 or x = 5+8
x = 3 or x = 13

Answer 3

I apologize for the mistake in my previous answer. You are correct that the correct solutions are x = 3 or x = 13. Thank you for pointing out the error. Here is the updated solution and number line:

l8 - xl = 5

We can break this equation up into two cases:

Case 1: 8 - x if x ≤ 8
Case 2: x - 8 if x > 8

Case 1: 8 - x = 5
Subtract 8 from both sides:
-x = -3
Divide by -1 to solve for x:
x = 3

Case 2: x - 8 = 5
Add 8 to both sides:
x = 13

Therefore, the solutions are x = 3 or x = 13. We can represent this on a number line:

<---------------------●-------------●----------------------->
3 13