WRITING INEQUALITIES FOR THE UNSHADED REGION SHOWN IN THE GIVEN FIGURE

Equation of horizontal lines will be in the form,

y = a or y = -a

Equation of vertical lines will be in the form,

x = a or x = -a

Equation of slanting line will be in the form

a x + by = c

The following inequalities can be used,

≤

≥

Less than

Greater than

Less than or equal to

Greater than or equal to

We have to use < or > sign when we have dotted line.
We have to use ≤ or ≥ sign, when we have solid line.

Write the inequalities to represent the following unshaded regions :

Problem 1 :

Solution :

The unshaded region is the third quadrant. All the values of x is lesser than 0 and values of y are less than 0. Then,

x ≤ 0 and y ≤ 0

Problem 2 :

Solution :

The given line is the horizontal line, it will be in the form y = a. The horizontal line passes through 2. Writing it as linear function, y = 2.

By considering the unshaded region, the values are greater than 2. So, the inequality representing the unshaded region is

y ≥ 2

Problem 3 :

Solution :

The given line is the vertical line, it will be in the form x = a. The horizontal line passes through -3. Writing it as linear function, x = -3.

By considering the unshaded region, the values are lesser than -3. So, the inequality representing the unshaded region is

x > -3

Problem 4 :

Solution :

The shown lines are vertical lines. Both are solid lines. Then we can use ≤ or ≥ signs based on the unshaded region. writing as linear functions, we get

x = 4 and x = 0

To the right of x = 0, the unshaded region is greater than 0. Considering to the left of 4, all the values are lesser than 4. Then inequality representing the unshaded region is

x ≥ 0 and x ≤ 4

Problem 5 :

Solution :

The shown lines are horizontal lines. Both are dotted lines. Then we can use < or > signs. By writing linear functions, we get

y = -2 and y = 3

Now by considering the unshaded region,

all the values above y = -2 are greater than -2.
all the values below y = 3 are lesser than 3.

Representing as inequalities, we get

y > -2 and y < 3

(or)

-2 < y < 3

Problem 6 :

Solution :

In the lines shown above, one line is horizontal line and another is a vertical line. Writing the linear function, we get

Equation of horizontal line is y = 2
Equation of vertical line is x = 3

Considering the unshaded region, all the y values below y = 2 are smaller than 2.

All the x values towards left of 3 are lesser than 3.

Representing as inequalities, we get

0 ≤ y ≤ 2 and 0 ≤ x ≤ 3

Problem 7 :

Solution :

The unshaded region is in the first quadrant. Considering the linear function x = 0, the values of y are greater than 0.

Considering the linear function y = 0, the values of x are lesser than 0.