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Solve and graph the inequalities below. There are several options for submitting your graphs. Please choose one of the options below:

A.)Create the graphs in a drawing program or using the whiteboard feature and attach them.
B.)Draw the graphs by hand and fax them or mail them to your instructor
C.)Describe your graphs using words as shown in the lesson.

1.) 2x > -6 and x – 4 < 3
2.) x + 5 > 2x + 1 and -4x < -8
3.) -3x < -6 or x + 5 < -2
4.) x - 2 > 2x + 1 or -2x - 2 < -10
please do work by hand a submit pictures

Respuesta :

Answer:


Step-by-step explanation:

1. We have the inequalities 2x > -6 and x-4<3

So, we get,

2x > -6 ⇒ x > -3 and x-4<3 ⇒ x < 7.

Thus, the solution is given by x > -3 and x < 7 i.e. -3 < x < 7 given by figure 1.

2. We have the inequalities x + 5 > 2x + 1 and -4x < -8

So, it gives us,

x + 5 > 2x + 1 ⇒ 4 > x i.e. x < 4 and -4x < -8 ⇒ x > 2.

Then, the solution is given by x < 4 and x > 2 i.e. 2 < x < 4 given by figure 2.

3. We have the inequalities -3x < -6 or x+5 < -2

The solution is,

-3x < -6 ⇒ x > 2 or x+5 < -2 ⇒ x < -7.

Thus, the solution is given by x > 2 or x < -7 given by figure 3.

4. We have the inequalities x-2 > 2x+1 or -2x-2 < -10

We get,

x-2 > 2x+1 ⇒ x < -3 or -2x-2 < -10 ⇒ -2x < -8 ⇒ x > 4

So, the solution is given by x < -3 or x > 4 given by figure 4.

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