How do you solve -6abs(5-2y) = -9?
1 Answer
Aug 23, 2015
Explanation:
Start by isolating the modulus on one side of the equation. This can be done by dividing both sides by
(color(red)(cancel(color(black)(-6))) * |5 - 2y|)/color(red)(cancel(color(black)(-6))) = ((-9))/((-6)
|5 - 2y| = 3/2
Since you're dealing with the absolute value of an expression, you must take into account the fact that the expression can be negative or positive.
5-2y>0 implies |5-2y| = 5 - 2y
Your equation becomes
5 - 2y = 3/2
2y = 5 - 3/2
y = (10 - 3)/2 * 1/2 = color(green)(7/4)
5 - 2y <0 implies |5 - 2y| = -(5-2y)
This time, the equation becomes
-(5 - 2y) = 3/2
-5 + 2y = 3/2
2y = (3 + 10)/2
y = 13/2 * 1/2 = color(green)(13/4)
Your original equation has two possible solutions,
y = 7/4" " or" "y = 13/4
