## Factoring inequalities deals with factoring the linear equation with the inequality sign. Factoring is the process of calculating the variable value with the help of quadratic formula and factor the common variable from the given linear expression. Inequality is the process of comparison of two or more values. Factoring inequalities involves the process of solving the linear expression in the quadratic form with inequality sign. The following are some of the examples with detailed solutions for factoring inequalities.

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## Examples problems on factoring inequalities:

The factoring problems are discussed below with inequality sign.

**Example 1:**

Factoring the inequalities a ^{2} – 3a < 0

### Solution:

Given

a ^{2} – 3a < 0

Take X as common factor

a (a - 3) < 0

So the product x (x - 3) to be equal to zero, then we get

a < 0 or a - 3 < 0

Solve the above simple equations to obtain the solutions.

a < 0

or

a < 3

** a< 0 or 3 is the solution.**

** Example 2:**

Factoring inequalities a ^{2} - 5 a + 6 > 0

**Solution:**

To factorize the expression, we write the equation x ^{2} - 5 a + 6 in the form factor

a ^{2} - 5 a + 6 > (a + x)(b + y)

So the sum of x and y is -5 and their product is 6. The integers that satisfy these conditions are - 2 and - 3. Hence

a ^{2} - 5 a + 6 > (a - 2)(a - 3)

Substitute into the original equation and solve.

(a - 2)(a - 3) > 0

(a - 2)(a - 3) is equal to zero if

a - 2 > 0

or

a - 3 > 0

Solve the above equations to get the solution

a > 2

or

a > 3

** a> 2 or 3 is the solution.**

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## Practice problems on factoring inequalities:

Practice problems for factoring inequalities are given below with answers.

** 1) **Factoring inequalities a ^{2} - 6 a + 9 > 0

**Answer: a = 3 is the solution.**

** 2) **Factoring inequalities a ^{2} – 6a > 0

**Answer: **** a="0" or 6 is the solution.**

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