This one is hard.
5 - |3-2x|/3 = 4
How do I begin to do this?
-|3-2x|/3 = -1
-|9-6x| = -3 or -|9-6x} = 3
????
from -|3-2x|/3 = -1
|3-2x|/3 = 1
|3-2x| = 3
now 3-2x = 3 OR -3+2x = 3
-2x = 0 or 2x = 6
x = 0 or x = 3
sub back in to see if they work, they both do.
Continuing from -|3-2x|/3 = -1
-(1/3)*|3-2x| = -1
Multiply both sides by -3
|3-2x| = 3
To solve this equation, follow these steps:
Step 1: Isolate the absolute value expression.
We have: -|3-2x|/3 = 4
To isolate the absolute value expression, we need to get rid of the fraction. Multiply both sides of the equation by 3:
-|3-2x| = 12
Step 2: Remove the negative sign from the absolute value expression.
Since the left side of the equation is already negative, we can remove the negative sign without changing the equation:
|3-2x| = -12
Step 3: Solve for two possible cases.
An absolute value expression can evaluate to either its positive value or its negative value. Therefore, we need to solve for both cases separately:
Case 1: The absolute value expression evaluates to its positive value:
|3-2x| = 12
Remove the absolute value notation:
3-2x = 12
Simplify:
-2x = 12 - 3
-2x = 9
Divide both sides of the equation by -2:
x = 9 / -2
x = -4.5
Case 2: The absolute value expression evaluates to its negative value:
|3-2x| = -12
Since the absolute value cannot be negative, this case has no solutions.
Therefore, the solution to the original equation is x = -4.5.