A teenager asks their friend to solve the equation 3−5k=12
. Their friend claims that subtracting 3
from both sides of the equation and then dividing both sides of the equation by −5
will give the solution to the equation. Are they correct?
Let's see if their friend's method is correct:
Starting with the equation 3 - 5k = 12.
Their friend suggests subtracting 3 from both sides:
(3 - 3) - 5k = 12 - 3
0 - 5k = 9
-5k = 9
Now their friend suggests dividing both sides by -5:
-5k / -5 = 9 / -5
k = -9/5
So their friend claims that k = -9/5 is the solution.
However, their friend's method is incorrect. When dividing both sides of an equation by a negative number, the direction of the inequality changes. In this case, dividing both sides by -5, we get:
(-5k) / -5 = 9 / -5
k = -9/5
The correct solution to the equation 3 - 5k = 12 is k = -9/5.