Introduction to algebra answers now:

Algebra is one of main part of mathematics in which it deals with solving the algebraic expressions in order to find the unknown variable value. Algebra mainly involves finding the unknown variable value with the reference of known values. In algebra alphabets are used to represents variables and the integers are considered as constants. Now we are going to solve the algebraic expressions to get the unknown variable answers. Now the solutions discussed below are in detail.

 

Answers for example algebra problems:

 

Example 1:  Solve the algebraic equation

          5(-3z - 2) - (z - 3) = -4(4z + 5) + 13

Solution:

Given algebraic expression is

5(-3z - 2) - (z - 3) = -4(4z + 5) + 13

Multiplying the above factors

-15z - 10 - z + 3 = -16z - 20 +13

Now combining the above terms we get

-16z - 7 = -16z - 7

Add 16z + 7 on both sides of the above expression then the equation becomes,

0 = 0

The above result shows that x is applicable for all real values. So the given expression is satisfies all real values.

Example 2: Simplify the algebraic expression

2(x -3) + 4y - 2(x -y -3) + 5

Solution:

Given the algebraic expression

2(x -3) + 4y - 2(x -y -3) + 5

Multiplying the integer terms

= 2x - 6 + 4y -2x + 2y + 6 + 5

Now grouping the above terms we get

= 6y + 5 is the solution

Example 3: When a <2, solve

|a - 2| - 4|-6|

Solution:

Given expression is

|a - 2| - 4|-6|

When a < 2 then a - 2 < 2 and if a - 2 < 2 the |a - 2| = -(a - 2).

Now substitute |a - 2| by -(a - 2) and |-6| by 6

|a - 2| - 4|-6| = -(a - 2) -4(6)

      |a - 2| - 4|-6| = -a -22 is the solution.

 

Answers for practice algebra problems:

 

1) Solve the algebraic equation     -4(y + 2) = y + 9

Answer: y = -17/5 is the solution.

2) Solve the algebraic equation -2(a - 1) – 4a - 1 = 3(a + 2)

Answer: a = - 5/9 is the solution.