Algebra - Solving Inequalities

Representing on a number line

100

Draw on a number line

x<-1

a circle on -1 with arrow pointing left

200

Draw on a number line

x≥2

a full circle on 2 with arrow pointing right

300

Draw on a number line

-3≤x<1

full circle on -3 and circle on 1 with a joining line.

400

Draw on a number line

x<-3 and x>3

circle on -3 with arrow pointing left

circle on 3 with arrow pointing right

500

Draw on a number line

0≤x<5 and  -2<x <4

full circle on 0 and circle on 5 with joining line

circle on -2 and 4 with joining line

Listing integers

100

List the integers which satisfy

x<5 and x>-3

-2,-1,0,1,2,3,4

200

List the integers which satisfy

0≤x<5 and 3≤x≤7

3,4

300

List the odd integers which satisfy

-4≤x<3 and -6≤x≤2

-3,-1,0,1

400

What is the lowest integer to satisfy this inequality? 

  6x +13 > 62

9

500

List the integers that satisfy both these inequalities.

2x + 4 < 0     and x > −7

-3,-4,-5,-6

Solving Inequalities

100

Solve

x+12>-7

x>-19

200

4x + 6 ≤ 18

x≤3

300

Solve:  3x+2x+7<11

x<1

400

Solve: 4(2x − 3) ≥ −8

x ≥ 1/2

500

Solve: (2x-6)/4  < 1

x<5

Solving Compound Inequalities

100

18 ≤ x + 20 < 39

-2 ≤ x < 19

200

Solve: 37 > 12x + 1 ≥ 13

3 > x ≥ 1

300

Solve: −34 > 8x + 6 > −82

−5 > x > -11

400

Solve 12 ≤4x/3<20

9 ≤x<15

500

Solve 4<(3x-1)/2<7

3<x<5

Solving inequalities with unknowns on both sides

100

Solve  2x - 5 < x - 1

x<4

200

Solve 5x + 1 ≤ 2x – 11

x≤ -4

300

Solve 4x+2x + 2 ≥ 3x + 3

x ≥1/3

400

Solve 6x-2> 4(x+8)

x>17

500

6(2x-3) < 2(x+6)

x<3