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Question

1.

-7y - 17 > 11

Part 1: Solve the inequality above.

Part 2: Describe the graph of the solution.

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2.

16 < 3x + 1 < 4

Part 1: Solve the inequality above.

Part 2: Describe the graph of the solution.

Answer 1

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1. the inequation is

- 7y - 17 >11

- 7y > 16

- y >16/7

y <- 16/7

so inequation will be satisfied for for any y >-16/7 for any real value of x...take any value of x and any value of y such that y > -16/7 , plot them on a graph paper ,then you will get an area or section..that's the required graph.

clearly the graph will be a section (area) which will lie above the straight line y = -16/7 and wouldn't touch (x,-16/7)..the section can exist till x exists.

2) similarly the inequation

16 < 3x + 1 < 4

15<3x<3

5<x<1

clearly the inequation is satisfied for any value of x which lies in this open interval (and for any real value of y)

now take any value of y (real) and take any value of x which lies in that interval. plot them on a graph paper..you will get a graph (a section) which doesn't touch x = 1 and x = 5. this is the required graph.

Answer 2

-7y-17>11

-7y-17+17>11+17

-7y>28

-7y/-7<28/-7

y<-4 anything that is <-4 would be shaded for the complete solution with a dotted line at

y=-4

16<3x+1< 4 16<3x+1-1<4 16-1<3x+1-1<4-1 15<3x< 3 5<x<1 anything between x<5<1 would be shaded excluding 5 and 1

Answer 3

1. -7y - 17 > 11

-7y > 28

y < -4

A circle at -4, and an arrow to the left.

2. 16 < 3x + 1 < 4

15 < 3x < 3

5 < x < 1

This doesn't make sense.

Maybe you meant 16 < 3x + 1 < 4?

Then the solution is 5 > x > 1.

The graph consists of open circles at 5 and 1, and a line segment connecting them.