*An equation is a mathematical sentence that has two equal sides separated by an **equal sign** (=). *

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Junior Class **Mathematics**

TOPIC: **Solving **Equations-

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**What is Equation?**

An equation is a mathematical sentence that has two equal sides separated by an **equal sign** (=).

**Example: 1**.

4 + 6 = 10 is an equation.

**Example: 2**.

12n = 24

Note that, 12 is the **coefficient** of **‘n’** in the above equation, while **‘n’** is a variable.

(**Variable** is a letter that represents an unknown number. And **coefficient** is the multiplicative factor of **another ****number** (variable), usually unknown).

That is, 12n ---> **12** is the coefficient of **n**. And **n** is unknown number called **variable**.

I hope you now understand?

That is brilliant!

Furthermore, **Equation** is an algebraic sentence which has an **equals ****sign** (=).

Let take more examples and analysis them;

1. x + 3 = 7 ( here **x** is a variable and the coefficient of **x** = 1)

2. 3a + 5 = 12 (here, **a** is a variable and the coefficient of **a** = 3)

3. x/4 = 5 (here, **x** is a variable and the coefficient of **x** = ¼)

4. 2m/3 = 13 -5(here, **m** is a variable and the coefficient of **m** = 2/3)

****You** **can** **go** **over** **it** **once** **again**, **but** **slowly** **this** **time*** .*****

Haven’t understood how to identify **variables** and **coefficient** in an equation then let try solving the equations.

**Here**** ****we**** ****go****!**

1. 12n = 24, find the value of n.

To solve for **n** you will need to divide both sides of the equation by the coefficient of **n**.

*Then, what **is** **the** **coefficient** **of** **n** **in** **the** **equation**?*

Correct! Coefficient of n = **12**.

That is, 12n/**12** = 24/**12**

And, n = 2.

2. x + 3 = 7, what is the value of x?

(**N****.****B****: ***the coefficient of **x** is **1** **and** you'll recall that any number divided by **1** is same number*).

Therefore, you need to take **3** to the Left-hand side of the equation. An that is possible by subtracting **3** from both sides on the equation.

That is:

x + 3 **- 3** = 7 **- 3**

Then, **x** = 4.

3. 3a + 5 = 12, find a.

Collet like terms by subtracting 5 from both sides of the equation.

That is, 3a + 5 **- 5** = 12 **- 5**

To get, 3a = 7

Divide both sides by the coefficient of **a**. When coefficient of **a** is 3.

Hence, 3a/**3** = 7/**3**

Then, **a** = 2 1/3 ( two whole number, one over three).

4. x/4 = 5 , what is the value of x?

First you multiply both sides of the equation by the **inverse** of the **coefficient** of **x**.

Also, note that **inverse** of ¼ = 4/1 and inverse of 2/3 = 3/2.

Therefore, *x*/4 x **4/1** = 5 x **4/1**

Then, ** *** x* = 20.

5. 2m/3 = 13 -5, find the value of m.

This is same as: 2m/3 = 8. ** Think**?

**Hence**, multiply both sides by the inverse of the coefficient of **m**. Which is **3/2**.

2m/3 x **3/2** = 8 x **3/2**

Therefore, **m** = 4 x 3

And, **m** = 12.

You can review the lesson over and over and you can as well drop your comment in the comment link bellow.

Thanks for having.

Watch out for the next class,

Yours truly,

**Shobowale**** Abdulateef.**

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