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How do you solve #- 7< 5 - 2y <= 1?#

Answer 1

Eli Assouline

Shown below

Treat it like a normal linear equation question:

#-7< 5-2y <=1 #

Get rid of the #5# in the middle by -5 on each of the terms

#-7 color(red)(" "-5 ) < 5 -2y color(red)(" "-5) <= 1color(red)( " "-5) #

#=> -12 < -2y <= -4 #

Divide each term by -2 to isolate #y#

When you divide by a negative number, the inequalities swap

#=> 6>y>=2 #

#=> color(blue)( 2 <= y < 6 ) #

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Answer 2

Hazel Anglin

#y in [2,6)#

we have #-7<5-2y<=1# subtracting 5 on both sides #-12<-2y<=-4# dividing 2 both sides #-6<-y<=-2# multiplying -1 both sides #6>y>=2# we get a range of y such that greater than equal to 2 and less than 6 also hence #y in[2,6)#

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Answer 3

Avery Alexander

To solve the compound inequality -7 < 5 - 2y ≤ 1:

Start by solving the inner inequality, 5 - 2y ≤ 1: Subtract 5 from both sides: -2y ≤ 1 - 5 -2y ≤ -4 Divide both sides by -2. Since we divide by a negative number, we flip the inequality sign: y ≥ -4 ÷ -2 y ≥ 2
Now solve the outer inequality, -7 < 5 - 2y: Subtract 5 from both sides: -7 - 5 < -2y -12 < -2y Divide both sides by -2. Since we divide by a negative number, we flip the inequality sign: 6 > y

Therefore, the solution to the compound inequality is 6 > y ≥ 2.

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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 #- 7&lt; 5 - 2y &lt;= 1?#

How do you solve #- 7< 5 - 2y <= 1?#