**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***:**1

*km*= 1000

*m*

**If two quantities are unequal, the symbol ‘≠’ (is not equal) is used.**

2.

2.

*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***:**8

*x*, -7

*y*, 0.5

*y*, 3

*a*, …..

**A**

2.

2.

**linear algebraic expression**contains two or more linear algebraic terms which are joined by a plus or minus sign.

*Example:*3

*x*– 4*y*, 4*x*+ 9, 6*x*– 2*y*+ 5, ……**A l**

3.

3.

**inear equation**is an equation involving numbers and linear algebraic terms.

*Example***:**

5

*x*– 4 = 11, 4*x*+ 7 = 15, 3*y*– 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:**

*x*+ 4 = 12

*x*= 12 – 4 ← (When +4 is moved to the right of the equation, it becomes –4)

*x*= 8

*Example***2:**

*x*– 7 = 11

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

*x*= 18

ExampleExample

**3:**

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

ExampleExample

**4:**

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