Question

Solve and graph each inequality -2y+7<1 or 4y+3<-5​

Answer 1

y < -2 or y > 3

Explanation:

`(1)\\\\-2y+7<1\qquad\text{subtract 7 from both sides}\\-2y+7-7<1-7\\-2y<-6\qquad\text{change the signs}\\2y>6\qquad\text{divide both sides by 2}\\\boxed{y>3}\\\\(2)\\\\4y+3<-5\qquad\text{subtract 3 from both sides}\\4y+3-3<-5-3\\4y<-8\qquad\text{divide both sides by 4}\\\boxed{y<-2}\\\\\text{From (1) and (2) we have:}\ y<-2\ or\ y>3`

`<,\ >-\text{op}\text{en circle}\\\leq,\ \geq-\text{closed circle}`

Answer 2

• 3 < y
• y < -2

Explanation:

1. -2y+7 < 1

Add 2y-1:

6 < 2y

Divide by 2:

3 < y

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2. 4y +3 < -5

Subtract 3:

4y < -8

Divide by 4:

y < -2

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These are graphed on the number line with open circles because y=-2 and y=3 are not part of the solution set.