To make the equation true for no values of x, we need to make sure that the left-hand side and the right-hand side are not equal for any value of x.
Let's simplify the left-hand side of the equation first:
1/3(12x + 18) + x
= 4x + 6 + x
= 5x + 6
To make this equation true for no values of x, we need to find an expression that is never equal to 5x + 6. One way to do this is to take the negative of 5x + 6:
-(5x + 6)
Now the full equation is:
1/3(12x + 18) + x = -(5x + 6)
We can simplify the left-hand side again:
1/3(12x + 18) + x
= 4x + 6 + x
= 5x + 6
And substitute it into the equation:
5x + 6 = -(5x + 6)
Simplifying this equation gives:
10x + 12 = 0
Dividing both sides by 10 gives:
x + 6/5 = 0
x = -6/5
So the original equation, 1/3(12x + 18) + x = -(5x + 6), is true for no values of x.