Inequalities

Question 1

What happens to an inequality when its multiplied or divided by a negative number?

Answer 1

The inequality sign must be reversed

Question 2

Inequality equations must be added, but what must they have in common?

Answer 2

The inequality signs need to face the same way

Question 3

Like variables can be added + subtracted, but they cant..

Answer 3

be multiplied and divided

Question 4

if |x| is > b and b is positive, then

Answer 4

x > b or x < - b

on number line, extends for infinity on both sides

Question 5

if |x| is >/ b and b is positive, then

Answer 5

x >/ b or x </ - b

on number line, extends for infinity on both sides

Question 6

if |x| is < b and b is positive, then

Answer 6

negative b < x < b

does not extend to infinity, confined area on number line

Question 7

if |x| is </ b and b is positive, then

Answer 7

negative b </ x </ b

does not extend to infinity, confined area on number line

Question 8

If a ≤ x ≤ b and c ≤ y ≤ d, to find the maximum value of xy and minimum value of xy..

Answer 8

evaluate the following four quantities:

• ac
• ad
• bc
• bd

the max and min will be largest and smallest of the four

Question 9

How to solve an equation in absolute form that is set equal to another equation in absolute form

Answer 9

1. solve for variable setting values equal to each other [.i.e. both positive or both negative]
2. solve for variable setting values opposite to each other [i.e. one negative and one positive]

Question 10

What will always be true about the sum of the absolute value of two numbers a and b?

Answer 10

|a+b|≤ |a| + |b|

a + b | ≤ | a | + | b |

Question 11

Absolute value of the sum of two quantities will be equal when…

Answer 11

1. both numbers are 0 or
2. both numbers are the same sign

Question 12

What will always be true about the subtraction of the absolute value of two numbers a and b?

Answer 12

|a-b|≥|a| - |b|

Question 13

Absolute value of the subtraction of two quantities will be equal when..

Answer 13

1. the second quantity is 0 or
2. both quantities are the same sign and the absolute value of the first quantity is greater than or equal to absolute value of second quantity

Question 14

If the absolute value of x is less than or equal to some positive number b, then x is less than or equal to b and greater than or equal to negative b.

Answer 14

|x|<b : -b < x < b
|x|≤ b: -b ≤ x ≤ b

on a number line, the points converge to one connected line that is limited

Question 15

If the absolute value of x is greater than or equal to some positive number b, then x is greater than or equal to b and less than or equal to negative b.

Answer 15

|x|> b : -b > x > b
|x|≥ b: -b ≥ x ≥ b

on a number line, the points do not converge and go on in infinity in opposite directions

Question 16

What is peculiur about this equation |x+7| = -2

Answer 16

If the absolute value of an expression is equal to a negative number, there will be no solutions to that equation.

Question 17

What is a step that should be taken when obtaining solutions to absolute value equations?

Answer 17

ALWAYS plug the solutions back in to see that the solution actually works. be wary of extraneous solutions ‘fake’ solutions