Integer Linear Problem

Introduction to integer linear problem:

Integer linear problem can be solved under linear algebra category. The linear expression with integer term is called as integer linear function. The linear problem associates with the families of vectors called linear spaces, and the expression has the general form as input one vector and output one vector, based to certain rules.

Linear problem has the demonstration in analytic geometry and their functions with integer can be generalized in operator theory. The following are the examples for linear integer problem.

Example Problems in Linear Integer:

Example 1:

Solve the linear expression -2(c - 3) – 4c - 1 = 3(c + 4) - c

Solution:

Given expression is
-2(c - 3) – 4c - 1 = 3(c + 4) - c

Multiplying the integer terms
-2c + 6 – 4c - 1 = 3c + 12 - c

Grouping the above terms
-6c + 5 = 2c + 12

Subtract 5 on both sides
-6c + 5 - 5 = 2c + 12 -5

Grouping the above terms
-6c = 2c + 7

Subtract 2x on both sides
-7c – 2c = 2c + 7 -2c

Grouping the above terms
-9c = 7

Multiply -1/9 on both sides
C = - 7/9

C= - 7/9 is the solution for the given equation

Example 2:

Solve the linear expression     -5(k + 2) = k + 9

Solution:

Given expression is
-5(k + 2) = k + 9

Multiplying the factors in left term
-5k - 10 = k + 9

Add 10 on both sides
-5k - 10 + 10 = k + 9 + 10

Grouping the above terms
-5k = z + 19

Subtract k on both sides
-5z - k = k + 19 -k

Grouping the above terms
-6k = 19

Multiply -1/6 on both sides
K = -19/6

K = -19/6 is the solution for the given equation

Practice Problems for Linear Integer:

1) Solve the linear expression -5(z - 3) – 2z - 3 = 2(z + 1) – 3z

Answer: z = 13/4 is the solution for the above given equation

2) Solve the linear expression     -7(b - 2) – 2b - 2 = 5(b + 2) – 5b

Answer: b = 2/9 is the solution for the given equation