## Notes on pre algebra

**Introduction :**

The purpose of notes on math pre algebra is to strengthen our arithmetic skills and to give you an introduction to basic algebra concepts, math vocabulary, and algebraic operations in preparation for an notes on pre algebra course. It is intended to ease students’ transition from Basic Mathematics into Elementary Algebra. Operations on real numbers, linear equations, graphing polynomials and factoring will be covered. Let us see Problems for notes on pre algebra.

Notes on pre algebra:

**EXAMPLE 1:**

**Solve: 9x - 5 = 68**

**Solution:**

Given, 9x - 5 = 68

9x = 68 + 5

9x = 73

x = `73/9`

or

**x = 8.11.**

**EXAMPLE 2 :**

**One third of a certain number is 18. find exact value of that unknown number.**

**Solution:**

let us assume unknown number be "x" . one third of x is ( 1/3 ) * x

so, ( 1/3 ) * x = 18

x = 18 * 3

x = 54

**the number is 54.**

**EXAMPLE 3:**

**Find the value of the expression 5x + 7 , if x = 6**

**Solution:**

Substitute x = 6 in the given expression 5x + 7

5x + 7 = 5(6) + 7

= 30 + 7

**X = 37**

Here the value of the expression is 37.

Notes on pre algebra:

**EXAMPLE 4**:

**If five times of a number is equal to 40. Then find what exactly the number is?**

**Solution:**

let us assume the unknown number as " X "

Given 5 * X = 40.

Move left side term to right

Then X =` 40/5`

The unknown number x is

**X = 8.**

**EXAMPLE 5:**

**Given : simplify**

18x - 4(16x-10x+2)+x.

**Solution:**

First we need to simplify the brackets. So we multiply (18x-10x+2) with 4

So, 72x - 48x + 40x - 8 + x.

It can be written as 72x - 48x + 40x + x - 8.

**So, the answer is 65x - 8.**

**EXAMPLE**

**6:**

**Solve the following system:**

x + y = 13 - (1)

3x - y = 11 - (2)

**Solution:**

Solve the (1) equation

y =13 -x

substitute in (2)equation

3x - (14 - x) = 11

3x - 14 + x = 11

4x = 25

x = 25/4 = 6.25

substitute value of x in (1)equation

6.25 + y = 13

y = 6.75

**The solution is, (6.25, 6.75).**