**Introduction about studying intermediate algebra:**

Intermediate Algebra is a section of mathematics that substitutes letters for numbers & uses overview techniques to work out equations. It consists of topic as Algebraic expressions, set of Numbers, Operations on true numbers, Linear equation in One Variable, Linear inequalities, The slope of a line, Solving systems of linear equations in two variables, Polynomials and Polynomial functions, normal term, Complex Fraction and Factoring.Let us study about some intermediate algebra problems.

Let us study some common term of algebra intermediate topics are given below,

** 1.** Study equation and inequalities.

Inequalities means require of uniformity .It is easily find out from graph

** 2.** Polynomials.

Two or more monomials are represented by Polynomials

** 3.** Study about rational expression and equation.

Studying addition, subtraction and multiplication of rational expressions

** 4.** Graphs, function, and application.

**Algebra Example 1:** Find the value of the algebraic expression at the given value 3.5 + x when x = 6.5

**Solution:**

The given expression is, 3.5 + x

Inmplement the x value

= 3.5 + 6.5

= 10

**Algebra ** **Example 2:** Solve for the variable. X - 10 = 8

**Solution:**

X - 10 = 8

Add 10 on both sides

X -10 + 10 = 8 + 10

X = 18.

**Algebra Example 3:** Malini has 16 rupees. She buys fruits for 12 rupees. Find the remaining amount with her.

**Solution:**

We can write it as 16 – 12 = 4.

**Algebra ** **Example 4:** Solve this X + 25 > 10

**Solution:**

X + 25 > 10

Subtract 25 on both sides

X + 25 - 25 > 10 - 25

X > -15

**Algebra ** **Example 5:** Solve the equations by substitution method.3x – 5y = 15, y=2x + 2

**Solution:**

Substitute the expression 2x + 2 for y in the first equation and solve for x:

3x – 5y = 15

3x – 5 (2x + 2) = 15

3x – 10x – 10 = 15

-7x – 10 = 15

-7x – 10 + 10 = 15 + 10

-7x = 25

` (-7x) /( -7)` = `25 / -7 `

x = -3. 57.

Plug in -3.5 for x into the equation to find y’s value.

y = 2x + 2

y = 2 (-3.5) + 2

y = -7 + 2

y = - 5.

The solution to the system is **(- 3.5, - 5).** ** **