Linear Inequalities & Graph

1 step equation

100

2x ≥ 8

x ≥ 4

200

x/7 < 9 

x  < 63

300

24x ≤ 144

24x ≤ 144 

---     ----

24     24

x ≤ 6 

400

16 > x + 7 

16 > x + 7 

-7      -7 

  9 > x  or x < 9 

500

254 ≤ k - 89

254 ≤ k - 89

+89      +89

343 ≤ k or k ≥ 343

2 step equation

100

2x + 5 > 13 

2x + 5 > 13 

     -5      -5 

2x > 8 

x > 4

200

-3x - 7 < 9 

-3x - 7 < 9 

-3x < 16

---    ---

x >-16/3 or x >-5.33

300

x / 4 + 1 ≤ 10

x ≤ 36 

400

11 + 3/2x ≤ 17

x≤ 4

500

(-x - 6) / 4 ≥ 2

 

x  ≤ -14

Multi-step Equation

100

5y + 8y < 13

5y + 8y < 13

13y < 13

y < 1

200

b - 3 + 4 > 7

b - 3 + 4 > 7 

b + 1 > 7

b + 1 - 1 > 7 -1 

b > 6

300

-a +6a ≥ 4+ 6a

-a +6a ≥ 4+ 6a

5a ≥ 4 + 6a

-4 ≥  6a -5a

-4 ≥  1a

400

13 + 2g - 8 + 6 ≤ -7 - g

13 + 2g - 8 + 6 ≤ -7 - g

13 - 8 + 6 + 2g ≤ -7 - g

11 + 2g ≤ -7 - g

 2g + g  ≤ -7 - 11

3g ≤ -18

g ≤ -6

500

(-6d)/5 -3 +3 < 9 - (4d)/5 +3

d > -30

Distributive Property (Multiply)

100

-3( 2v -5) < -13

-6( 2v -5) < -13

-6v + 10 < -13

-6v + 15 -15 < -13-15

-6v < -28

v < 4.66 

200

-f ≤ -f + 7(f - 2)

-f ≤ -f + 7(f - 2)

-f ≤ -f + 7f - 14

-f ≤ -f + 7f - 14

-f ≤  6f - 14

14 ≤  7f

2 ≤  f

300

-2( 2+ 2h) -2 > 6

-2( 2+ 2h) -2 > 6

-4 -4h -2 > 6

-6 - 4h < 6

 - 4h < 12

h > -3

400

28 - 7k ≤ -4(-7k - 7)

28 - 7k ≤ -4(7k - 7) 

28 - 7k ≤ -28k + 28

28- 28 - 7k ≤ -28k + 28 -28 

0 + -7k + 7k ≤ -28k + 7k

0 + 0 ≤ -21k

0 ≥  k  

500

-3w -5( w +2 ) ≥ -3(w + 4) +6

-3w -5( w +2 ) ≥ -3(w + 4) +6

-8w -10 ≥ -3w -12 +6

-8w -10 ≥ -3w -6

-8w + 3w ≥  -6 + 10

-5w ≥  4

   w ≤ -4/5