Let's solve your equation step-by-step.
|n+9|=5n−3
Solve Absolute Value.
|n+9|=5n−3
We know either n+9=5n−3 or n+9=−(5n−3)
n+9=5n−3 (Possibility 1)
n+9−5n=5n−3−5n (Subtract 5n from both sides)
−4n+9=−3
−4n+9−9=−3−9 (Subtract 9 from both sides)
−4n=−12
(Divide both sides by -4)
n=3
n+9=−(5n−3) (Possibility 2)
n+9=−5n+3 (Simplify both sides of the equation)
n+9+5n=−5n+3+5n (Add 5n to both sides)
6n+9=3
6n+9−9=3−9 (Subtract 9 from both sides)
6n=−6
(Divide both sides by 6)
n=−1
Check answers. (Plug them in to make sure they work.)
n=3 (Works in original equation)
n=−1 (Doesn't work in original equation)
Answer:
n=3
