How do you solve abs(4y+5)=7?

1 Answer
smendyka
Dec 21, 2016

y = 1/2 and y = -3

Explanation:

Because the absolute value function transform positive or negative number into a positive number we need to solve the interior of the absolute value function for both the negative and positive form of its equality:

Solution 1)

4y + 5 = color(blue)(7)

4y + 5 - color(red)(5) = 7 - color(red)(5)

4y + 0 = 2

4y = 2

(4y)/color(red)(4) = 2/color(red)(4)

(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = 1/2

y = 1/2

Solution 2)

4y + 5 = color(blue)(-7)

4y + 5 - color(red)(5) = -7 - color(red)(5)

4y + 0 = -12

4y = -12

(4y)/color(red)(4) = -12/color(red)(4)

(color(red)(cancel(color(black)(4)))y)/color(red)(cancel(color(black)(4))) = -3

y = -3

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