Answer:
x = 4 or x = 1
Step-by-step explanation:
Solving absolute value equations can be a bit tricky. Absolute values are actually distance measurements. A very simple example is I x - 3 I = 2 says that "x is 2 units away from 3 on a number line". 2 units from 3 going to the right is 5, 2 units from 3 going to the left is 1. So in other words, absolute value equations will have 2 answers, in this case 2 units to the right (+2) and 2 units to the left (-2). That means that x - 3 = 2 OR x - 3 = -2. Let's start to solve this one:
5I 2x - 5 I - 3 = 12
Start by adding 3 to both sides:
5I2x-5I = 15
Now divide both sides by 5:
I2x-5I = 3
We will set the left side equal to both +3 and -3 to get our 2 solutions:
2x - 5 = 3 and 2x - 5 = -3
Solving the first one for x:
2x = 8 and x = 4
Solving the second one:
2x = 2 and x = 1.
Fit these into the original absoute value statement and see if they are both true:
5I2(4)-5I-3=12 --> 5I3I - 3 = 12 and 15 - 3 = 12
5I2(1)-5I-3 = 12 --> 5I-3I - 3 = 12. The absolute value of -3 is 3, so 15 - 3 = 12. They both check out@
