# 4.1 Linear Equations I

4.1 Linear Equations I

4.1.1 Equality
1. An equation is a mathematical statement that joins two equal quantities together by an equality sign ‘=’.
Example: km = 1000 m

2.
If two quantities are unequal, the symbol ‘≠’ (is not equal) is used.
Example: 9 ÷ 4 ≠ 3

4.1.2 Linear Equations in One Unknown
1. A linear algebraic term is a term with one unknown and the power of unknown is one.
Example: 8x, -7y, 0.5y, 3a, …..

2.
A linear algebraic expression contains two or more linear algebraic terms which are joined by a plus or minus sign.
Example:
3x – 4y, 4+ 9, 6x – 2y + 5, ……

3.
A linear equation is an equation involving numbers and linear algebraic terms.
Example:
5x – 4 = 11, 4x + 7 = 15, 3y – 2 = 7

4.1.3 Solutions of Linear Equations in One Unknown
1. Solving an equation is a process of finding the values of the unknown in the equation.
2. The number that satisfies the equation is called the solution or root of the equation.
Example 1:
+ 4 = 12
x = 12 – 4 ← (When +4 is moved to the right of the equation, it becomes –4)
= 8

Example 2:
– 7 = 11
x = 11 + 7 ← (When –7 is moved to the right of the equation, it becomes +7)
= 18

Example
3:

$\begin{array}{l}8x=16\\ x=\frac{16}{8}←\overline{)\begin{array}{l}\text{when the multiplier 8 is moved}\\ \text{to the right of the equation, it}\\ \text{becomes the divisor 8}\text{.}\end{array}}\\ x=2\end{array}$

Example
4:
$\begin{array}{l}\frac{x}{5}=3\\ x=3×5←\overline{)\begin{array}{l}\text{the divisor 5 becomes the}\\ \text{multiplier 5 when moved}\\ \text{to the right of the equation}\text{.}\end{array}}\\ x=15\end{array}$