Question

Use real number line to find the range of values of x for which:

(i) x > 3 and 0 < x < 6.

(ii) x < 0 and – 3 ≤ x < 1

(iii) −1 < x ≤ 6 and −2 ≤ x ≤ 3

Answer 1

(i) x > 3 and 0 < X < 6

Both the given in equations are true in the range where their graphs on the real

number lines overlap.

The graphs of the given in equations can be drawn as:

x > 3

From both graphs, it is clear that their common range is

3 < x < 6

(ii) x < 0 and -3 ≤ x < 1

Both the given in equations are true in the range where their graphs on the real

number lines overlap.

The graphs of the given in equations can be drawn as:

X < 0

From both graphs, it is clear that their common range is

-3 ≤ x < 0

(iii) -1 < x ≤ 6 and -2 ≤ x ≤ 3

Both the given in equations are true in the range where their graphs on the real

number lines overlap.

The graphs of the given in equations can be drawn as:

− 1 < x ≤ 6

From both graphs, it is clear that their common range is

1 < x ≤ 3