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