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
