Junior Class Mathematics (Solving Equations)

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.