Solving & Graphing Two-Step Inequalities

when is it an open circle

<,>

-6x-15>3

X<-3

2x<9

X<4.5

2x-3<7

x<5

2x<-2=8

x<5

if you divide by a negative would your problem stay the same?

no, it will switch (flip) the sign

when is at a closed (filled in) circle

numbers are equal to

Open or close circle <,>?

open

< and > uses what type of circle

open circle

p-8<-2

p<-10

4-R> -5

r>-9

what is the frist step when solving Inequalities

simplify

x≥-4

solve -2x − 1 ≤ 7

x>7

solve -3x < -21

x≤-7

solve 1 - 7x ≥ 50

x≥-10

solve x + 4 ≥ -6

x≥10

solve x+3≥13

x≥-7

solve x+7 ≥ 0

x>-7

solve x/(-7) < 1

1-2t>t+10

t>3

If the inequality is -8<x, which way do you draw the arrow on the number line?

towards the larger numbers (right)

If the inequality is -4>x, which way do you draw the arrow on the number line?

towards the smaller numbers (Left)

If the inequality is 8>x, which way do you draw the arrow on the number line?

towards the smaller numbers (Left)

when do you make a non filled in circle

when the symbol is < or >

when do you change(flip) the sign

when you are multiplying or dividing by a negative

5x - 10 < -30

x < -4

2x < -10

x < -5

3-2x>17

x < -7

28 < 20 - 8x

x < 1

2x + 1 < 7

x < 3

8 + 2x < 6x + -20

x < 3

4x + 49 < 9 - x

x < 38

4x+6<3x-5

x <-11

-5x + 10 < 30

x > -4

-2x < 10

x > -5

9x - 99 > 18x

x > 11

5x + 2 > 3x +10

x > 4

x<-1

x+3<2

x>6

x/3 > 2

8+4x>9

x<-0.25

5+2x>7

x<-1

x+3<2

x<-1

8x+5<3x+2(1x+2)

x<-1/3

3+15x>8

x<-3

-3x>12

x<-4

33-4x>53+x

x<-4

8x<-32

x<-4

-4x-16>8

x<-6

4x<-24

x<-6

3-2x>17

x<-7

-2x-8>10

x<-9

10+5x>8

x<0.4

5x+5<10

x<1

2x+5<6

x<1/2 or x<0.5

10x+34<10,034

x<1000

3(x-7)<12

x<11

17+6x>5

x<2

5x<10

x<2

7-10x<27

x<2

-7x>-21

x<3

12x+3<39

x<3

2x+7<13

x<3

33x+11<22

x<3

5+15x<10

x<3

2+x<8

x<4

7+4x<-2x-31

x<4

-10+2x<70

x<40

47+x<90

x<43

1-x<5-3+43-2x

x<44

24-10x<74

x<5

3x+1<16

x<5

38x<266

x<7

3+4x<39

x<9

-6x+28<34

x>-1

2-9x<92

x>-10

-12x<24

x>-2

-2x>4

x>-2

3-2x>17

x>-7

4x+49<9-x

x>-8

2x+14>16

x>1

-5x-15<30

x>10

2x>24

x>12

18+6x<6

x>2

2x+3>7

x>2

2x>4

x>2

4x+2>10

x>2

4x+6>14

x>2

3+2x>7

x>2.5

-2x+10<50

x>20

13+5x>113

x>20

x+4>24

x>20

9x+9>36

x>3

2(x-2)>4

x>4

5x+2>3x+10

x>4

6x+2>4x+10

x>4

8x+7>39

x>4

3(5+2-3)+7x>40

x>40

2+x>57+32-x

x>43.5

x-1>4

x>5

5-5x>35

x>6

8x+2>58

x>7

3x+4>28

x>8

3(x-4)>15

x>9

3x-12>15

x>9

3y+1<16

y<5

3y-3>12

y>5

do you always have to have a circle on your number line?

yes

z/2+1<3/2

z<1

z-5<15

z<20

x≤2

−4x ≥ -8

Does a line under < change the direction on the arrow

no

Does a line under > change the direction on the arrow

no

M<6/2

M<3

x<-3

What is the inequality for the graph?

-2+-3x_>1

x_<-1

4x_<_-12

x_<_ -3

-2(x+4)≥8

x≤-8

5x+4≤9

x≤1

½x+4≤1.5x-7

x≤11

½x≤9

x≤18

-21≤-3(x+2)

x≤5

-5(x+1)≥-50

x≤9

12y-5<31

y<3

2n+8<24

n<8

-3n<18

n>-6

5n-4>11

n>3

12+3n>24

n>4

If you are multiplying or dividing a_____you always switch the inequality

negative

32-5>x+2

25>x

1-v>2+v

-1/2>v

28<4(5-2x)

-1>x

n2+(-10)>n7

-2>n

22>2(5-2x)

-3<x

3/4x+2=-1

-4

a/4=-12

-48

-16=4(h+5)

-9

(8+10)+(12- 15)<30x

.5<x

2x/34>6x

0>x

5x-22x+7<8x-31+12

1 1/3

91>8x+11

10>x

n< 1

12n+ 3 < 9n+ 4

1<x

12x+ 17< 17x+12

x>-2

13x- -9 > 10x + 7

3*11>462g

14>g

7=x/2-1

16

-4(2n-6)<n+6

2<n

(10+48)>10x+38

2>x

2(3x+4)>1(4+8x)

2>x

x>5

2x-3>7

-3x+3>6x

3>x

12>3x

4>x

42>6+9x

4>x

s<1

4s< s+3

36<5x+11

5<x

M+3<9

M<6

M>5+6

M>11

M>8*3

M>24

Open or closed circle? Left or right? x>3

Open/ right

If the inequality is 2<x, which way do you draw the arrow on the number line?

Towards the larger numbers (right)

x<-5

What is the inequality for the graph?

x<2

What is the inequality for the graph?

x<5

What is the inequality for the graph?

x>-3

What is the inequality for the graph?

x>2

What is the inequality for the graph?

x>5

What is the inequality for the graph?

x≤-3

What is the inequality for the graph?

x≤2

What is the inequality for the graph?

x≤5

What is the inequality for the graph?

x≥-3

What is the inequality for the graph?

x≥2

What is the inequality for the graph?

< and > underlined is what type of circle

closed circle

The inequality will change only if the ___________ is negative.

coefficient

what kind of circle do you have when the sign is > or <?

empty

7f<14

f<2

> stands for

greater than

> that is underline stands for

greather than or equal to

h/3<3

h<3

When do you switch the sign?

if you switch sides to get the variable from right to the left

j-36>78

j>114

-5k<30

k<-6

-5k<30

k>-6

Do you shade or move your graph left or right? x<2

left

< stands for

less than

< that is underline stands for

less than or equal to

m+6>10

m>4

2n+6<4

n<-1

n-5<-7

n<-12

n-5<-7

n<-2

n-5<15

n<20