Final answer:
To complete the equation so that it has exactly one solution, simplify and rearrange the terms. Distribute the 4/3, combine like terms, clear the fraction, combine like terms again, and solve for x. The completed equation is 4/3 (-9x+12)-x= - 31/42x - 9
Step-by-step explanation:
To complete the equation so that it has exactly one solution, we need to simplify and rearrange the terms.
Start by distributing the 4/3 to the terms inside the parentheses:
(4/3)(-9x) + (4/3)(12) - x = ___x - 9
This gives us:
-12x + 16/3 - x = ___x - 9
Next, combine like terms:
-13x + 16/3 = ___x - 9
Now, we want to eliminate the fractional coefficient 16/3. To do this, we can multiply the entire equation by 3 to clear the fraction:
3(-13x + 16/3) = 3(___x - 9)
Simplifying, we have:
-39x + 16 = 3x - 27
Finally, combine like terms and solve for x:
-42x = 31
x = -31/42