GRAPH INEQUALITIES ON A NUMBER LINE

Solve the inequalities and represent the possible values of the variable on a number line.

Problem 1 :

6 > z - 2

Solution :

6 > z – 2

Add 2 on both sides.

6 + 2 > z – 2 + 2

z < 8

Problem 2 :

g + 7 < -12

Solution :

g + 7 < -12

Subtract 7 on both sides.

g + 7 - 7 < -12 – 7

g < -19

Problem 3 :

d – 5 < 7

Solution :

d – 5 < 7

Add 5 on both sides.

d – 5 + 5 < 7 + 5

d < 12

Problem 4 :

15 > k + 2

Solution :

15 > k + 2

Subtract 2 on both sides.

15 - 2 > k + 2 – 2

k < 13

Problem 5 :

1 + x > -16

Solution :

1 + x > -16

Subtract 1 on both sides.

1 - 1 + x > -16 – 1

x > -17

Problem 6 :

y + 8 < -9

Solution :

y + 8 < -9

Subtract 8  on both sides.

y + 8 - 8 < -9 – 8

y < -17

Problem 7 :

8 ≤ 8 + r

Solution :

8 ≤ 8 + r

Subtract 8 on both sides.

8 – 8 ≤ 8 – 8 + r

r ≥ 0

Problem 8 :

w + 8 ≥ 11

Solution :

w + 8 ≥ 11

Subtract 8 on both sides.

w + 8 - 8 ≥ 11 – 8

w ≥ 3