Inequalities

Question 1

When can you add or subtract inequality equations?

Answer 1

When the signs (, etc) are the SAME

Question 2

When dividing or multiplying the inequality by a negative number, what happens?

Answer 2

The sign (>,etc) flips

Question 3

Can you divide or multiply an inequality by an unknown variable?

Answer 3

No unless you know if it’s positive or negative (to know when to flip the sign)

Question 4

What are the rules for a compound inequality (three-part inequality)?

Answer 4

Can be manipulated in the same way an equation can. What ever you do to one part must be done to the remaining three parts. When the compound inequality is divided or multiplied by a negative number, BOTH inequality signs must be flipped.

Question 5

If a<= x <= b and if c <= y <= d then what is the minimum and maximum value of xy?

Answer 5

Solve for ac ad bc and bd. The biggest is the max and the smallest is the min.

Question 6

What is an absolute value of a number?

Answer 6

The distance of the number from 0. We do not care if it’s positive or negative.

Question 7

|a+b| will always be what?

Answer 7

<= |a| + |b|

Question 8

When |a+b| = |a| + |b| and a and b are not equal to 0, then…

Answer 8

A and b share the same sign (both positive or both negative)

Question 9

|a-b| will always be what?

Answer 9

> = |a| - |b|

Question 10

When |a-b| = |a| - |b| and b is not equal to 0, then…

Answer 10

1) A and b share the same signs (both positive or both negative)

AND

2) |a| >= |b|

Question 11

If |x| > b,

Answer 11

Then x>b
Or
x < -b

Question 12

If |x| < b,

Answer 12

Then -b < x < b

Question 13

For any real number a, if a>0, then

|a| =

And

|-a| =

Answer 13

a

|-a|

Question 14

If two absolute values are equal, it must be true that what?

Answer 14

The expressions within the absolute value bars are either equal or opposite

Question 15

X^2 < b =

Answer 15

-rootb < x < rootb

Question 16

X^2 > b =

Answer 16

x > rootb
Or
x < - rootb

Question 17

Which inequalities represent (x-12)^2 > 169?

Answer 17

X^2 > 169
X > 13 OR X < -13

Fill in the value of x and you get:

X< -1
Or
X> 25

Question 18

For any real number a, if a<0, then

|a| =

And

|-a| =

Answer 18

-a

|a|

Question 19

If x^2 = |x|, then what must x be?

Answer 19

X must be 1,0, or -1

Question 20

How do you express the following statement: k is halfway between m and n on the number line

Answer 20

(m+n)/2 = k

Question 21

On a number line, the distance between c and y is:

Answer 21

|x-y|