Solve the absolute value equation. Graph the solution.
2|3x – 5| – 8 = 8
To solve the absolute value equation 2|3x – 5| – 8 = 8:
First, isolate the absolute value term by adding 8 to both sides:
2|3x – 5| = 16
Next, divide both sides by 2 to solve for the absolute value:
|3x – 5| = 8
Now, split the equation into two separate equations, one positive and one negative, to remove the absolute value brackets:
1) 3x - 5 = 8
2) -(3x - 5) = 8
Solve each equation separately:
1) 3x - 5 = 8
Add 5 to both sides:
3x = 13
Divide by 3:
x = 13/3
2) -(3x - 5) = 8
Distribute the negative sign:
-3x + 5 = 8
Subtract 5 from both sides:
-3x = 3
Divide by -3:
x = -1
Therefore, the solutions to the absolute value equation 2|3x – 5| – 8 = 8 are x = 13/3 and x = -1.
To graph the solution, create a number line and mark the two solutions (-1 and 13/3) on it.