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How do you solve #2y-9>5y+12#?

Answer 1

#y < -7#

First, isolate the #y# term on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced:

#2y - 9 - color(red)(2y - 12) > 5y + 12 - 9 - color(red)(2y - 12)#

#2y - 2y - 9 - 12 > 5y - 2y + 12 - 12#

#0 - 9 -12 > 5y - 2y + 0#

#- 9 -12 > 5y - 2y#

Now we can group the like terms:

#-21 > (5 - 2)y#

#-21 > 3y#

And lastly, we can solve for #y# while keeping the inequality balanced:

#(-21)/color(red)(3) > (3y)/(color(red)(3)#

#-7 > (color(red)(cancel(color(black)(3)))y)/color(red)(cancel(color(black)(3)))#

#-7 > y#

And to get this solution in terms of #y# we can reverse or "flip" the inequality:

#y < -7#

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Answer 2

Hazel Anglin

To solve the inequality 2y - 9 > 5y + 12, first, subtract 2y from both sides to isolate the variable term:

-9 > 3y + 12

Next, subtract 12 from both sides:

-21 > 3y

Finally, divide both sides by 3:

y < -7

So, the solution to the inequality is y < -7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #2y-9&gt;5y+12#?

How do you solve #2y-9>5y+12#?