Answer:
Option 4 - No solution exist
Step-by-step explanation:
Given : Expression \(3|-3x + 9| = -18\)
To find : What is the solution of the expression?
Solution :
Step 1 - Write the expression
\(3|-3x + 9| = -18\)
Step 2 - Divide the expression by 3 both side,
\(|-3x + 9| = -6\)
Step 3 - Break down the problem into two equation,
\(-3x + 9 = -6\) ....(1)
\(-(-3x + 9 )= -6\) ....(2)
Step 4 - Solving equation (1),
\(-3x + 9 = -6\)
\(-3x=-15\)
\(x=5\)
Step 4 - Solving equation (2),
\(-(-3x + 9 )= -6\)
\(3x-9=-6\)
\(3x=3\)
\(x=1\)
The values of x are x=1 and 5.
Step 5 - Now, We check the points in the equation
At x=1
\(3|-3(1) + 9| = -18\)
\(3|6| = -18\)
\(18
eq -18\)
At x=5
\(3|-3(5) + 9| = -18\)
\(3|-15+9| = -18\)
\(3|-6|
eq -18\)
The solution does not exist.
At x=1
\(3|-3(1) + 9| = -18\)
\(3|6| = -18\)
\(18
eq -18\)
The solution does not exist.
Therefore, The solution of the given expression does not exist.
So, Option 4 is correct.
