Linear Inequalities

Short Answer Type

1. Solve

Solution:

We have

Equation x-1 and x-3 to zero, we obtain x=1,-3 as critical points. Plot these points on real line as shown in fiqure.

The real line is divided into three regions. In the right most region the expression on LHS of (i) is positive and in the remaining two regions it is alternately negative and positive. Since the expression in (i) is positive, so the solution set is given by

.

2. Solve.

Solution:

We have,

[Transposing to LHS and 9 to RHS]

.

3. Solve

Solution:

We have

[Transposing to LHS and to RHS]