Question

1. x – 3 > –9

2. –2x + 1 ≤ –11

3. 10 < –3x + 1

4. 2(x + 5) > 8x – 8

5. –2(x – 3) ≥ 5 – (x + 3)

6. Explain, in complete sentences, when you would use an open circle or a closed circle, and when you would shade to the right or left, to graph an inequality on the number line.

Answer 1

7. Describe a real life scenario where inequalities are used and state the inequality.

Answer 2

1. x - 3 > - 9
x > -9 + 3
x > - 6
2. -2x + 1 <= - 11
-2x <= - 11 - 1
-2x <= - 12
x => -12/-2
x => 6
3. 10 < -3x + 1
10 - 1 < - 3x
9 < - 3x
9/-3 > x
-3 > x
4. 2(x + 5) > 8x - 8
2x + 10 > 8x - 8
2x - 8x > -8 - 10
-6x > - 18
x < -18/-6
x < 3
5. -2(x - 3) >= 5 - (x + 3)
-2x + 6 >= 5 -x - 3
-2x + x >= 2 - 6
-x >= - 4
x <= -4/-1
x <= 4

6. To graph an inequality on a number line :
An open circle is used if the inequality sign is greater then or less then. If there is an equal sign, then you do not use an open circle. A closed circle is used when an equal sign is present. It can be used if there is a greater then or equal to , or less then or equal to.
For instance, if you had x < 8 or x > 8, you would use an open circle.
If your inequality looked like this, x <=4 or x >=4, you would then use a closed circle.
As far as the shading goes....x < 4...this is saying that x is less then 4. If it is less then, the shading goes to the left. If the inequality stated x > 4...x is greater then 4, then the shading would go to the right.
example :
x < 5 -- open circle, shading to the left.
x >= 5 -- closed circle, shading to the right
x > 10 -- open circle, shading to the right
x <= 3 -- closed circle, shading to the left.

7. You are going to the store to buy some fruit. You have $5. You want to purchase apples and bananas.
a = apples and b = bananas
a + b <=5
Basically, all this is saying is that the apples plus the bananas has to be less then or equal to $5 in order for you to be able to purchase it without going over.