Solve the absolute value equation. Graph the solution.
2|3x-5| - 8 = 8
To solve the absolute value equation 2|3x-5| - 8 = 8, we can start by isolating the absolute value term.
Adding 8 to both sides, we get:
2|3x-5| = 16.
Then, we divide both sides by 2:
|3x-5| = 8.
This equation can be solved in two cases: when 3x-5 is positive and when 3x-5 is negative.
Case 1: 3x-5 > 0.
In this case, the absolute value can be removed by keeping the expression inside the absolute value unchanged. So we have:
3x-5 = 8.
Adding 5 to both sides:
3x = 13.
Dividing by 3:
x = 13/3.
Case 2: 3x-5 < 0.
In this case, the absolute value can be removed by changing the sign of the expression inside the absolute value. So we have:
-(3x-5) = 8.
Expanding the negative sign:
-3x + 5 = 8.
Subtracting 5 from both sides:
-3x = 3.
Dividing by -3:
x = -1.
Therefore, the solution to the absolute value equation is x = 13/3 and x = -1.
To graph the solution, we can plot these two values on a number line:
-1 -------------- 13/3
The solution set is x = {-1, 13/3}.
To solve the absolute value equation 2|3x-5| - 8 = 8, we can follow these steps:
Step 1: Add 8 to both sides of the equation:
2|3x-5| = 16
Step 2: Divide both sides of the equation by 2:
|3x-5| = 8
Step 3: Set up two separate equations and remove the absolute value:
3x-5 = 8 or 3x-5 = -8
Step 4: Solve each equation separately:
For the first equation, 3x-5 = 8:
Adding 5 to both sides:
3x = 13
Dividing both sides by 3:
x = 13/3
For the second equation, 3x-5 = -8:
Adding 5 to both sides:
3x = -3
Dividing both sides by 3:
x = -1
Therefore, the two solutions to the absolute value equation are x = 13/3 and x = -1.
To graph the solution, we can plot these two points on a number line:
-1 ----------------------- 13/3
So the graph of the solution would represent these two points on a number line.