absolute values: what am i do do with |2x+3| = 5

Re: absolute values

weaver32 said:
|2x+3| = 5

what am i to do here
Click to expand...
You need to understand the meaning of absolute value.

If the absolute value of "something" is 5, then that "something" must be either 5 or -5.

If
| 2x + 3 | = 5, then

2x + 3 = 5 or 2x + 3 = -5

Now, solve those equations for x. You'll end up with two possible values for x; both should check in your original equation.
 
weaver32 said:
|2x+3| = 5

what am i to do here
Click to expand...

You have what is called an absolute value equation.

How to solve:

1-Isolate the absolute value expression.

2-Create two new equations (I will call two cases). Here is the tricky part. You're actually going to make two separate equations from the original one. The first equation should look like the original, just without the bars on it. The second equation should like the first, only take the opposite of the right side of the equation.

3-Solve the new equations to get your answer(s). In other words, solve for x.

4-Plug your values for x into the original equation and simplify.

You were given:

|2x + 3| = 5

We now follow the steps above.

Case 1:

2x + 3 = 5

We solve for x.

2x = 5 - 3

2x = 2

x = 2/2

x = 1.

Case 2:

2x + 3 = - 5....Notice that this time, I equated the left side of the equation to NEGATIVE 5 NOT positive 5. See it?

2x = -5 - 3

2x = -8

x = -8/2

x = -4

We have two answers for x: x = 1 OR x = -4.

We now plug these two answers BACK INTO the original equation given and simplify.
If we get the SAME ANSWER on BOTH SIDES of the equation, then we are right.

Ready?

|2x + 3| = 5

Let x = 1.

|2(1) + 3| = 5

|2 + 3| = 5

5 = 5...It checks!

Next, let x = - 4.

|2x + 3| = 5

|2(-4) + 3| = 5

|-8 + 3| = 5

|-5| = 5

Absolute value is always POSITIVE.

This means that |-5| becomes 5.

So:

5 = 5...It checks!

Final Answer: x = 1 and x = -4.

Done!
 
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