Linear Inequalities

Question 1

What do you do when you multiply or divide by a negative in a linear inequality?

Answer 1

FLIP the inequality

Question 2

10 < 2x + 4 < 24 ?

Answer 2

when you done thing to anyone of these parts you have to do it to each of them so -4

6 < 2x < 20
then /2
= 3 < x < 10

** if this were negative you would flip ALL of the inequalities

Question 3

what does “at least” mean ?

Answer 3

> or equal to

Question 4

when you see 0 < x^2 < 1 what do you know about x?

Answer 4

you know that x can be a positive or negative because the x^2 will get rid of the negative sign

Question 5

if ab > 0 and a < 0 which of the following is greater than b?

1. -0.5
2. 0
3. .5

Answer 5

by looking at a <0 you know a is a negative so you can solve ab > 0 by dividing by a BUT you know a is a negative and when you divide by a negative you have to FLIP the sign so you get b < 0
SO anything greater than b would be 0 and .5

Question 6

If 7(x + 1) = 8(y - 1) and y and x are both positive integers, what is the least possible value of x + y?

A. 1
B. 2 
C. 7
D. 9 
E. 15

Where should you start with solving this in terms of PITA?

Answer 6

start with C and do x + y = 7 and then solve for x so x = 7 - y and then plug in that value for x and see if the equations are equal. Keep going until you find the correct answer.

Question 7

0 <= |x|/2 <= 8

QA: The absolute value of the least possible value of x

QB: The absolute value of the greatest possible value of x

A B C D

Answer 7

they are the same, C! x = -16 or 16 since they have the absolute value, the values are the same