An
equation is a mathematical statement that shows equality between two
expressions. There are different forms of equations; one of them is linear
equation.
A
linear equation is an equation on a straight line that contains one unknown.
Examples of linear equations are:
(a) 2x + 6 = 16
(b) 3x – 9 = 4x – 25
(c) 3(y + 2) = 8y + 10
Terms used in linear equation:
i.
Unknown: This is usually letters and it denotes missing number i.e x,
y, etc.
ii.
Co-efficient: This a number placed together with unknown e.g. 2a, 3y.
iii.
Like terms: Terms are separated by addition or subtraction in an
expression. So like terms are terms that can be combined.
Using
different operations, linear equations are solved by finding values of
different variables which are unknowns.
We must note that equations can be solved by;
1.
Adding the same number to both sides of the equation.
2.
Subtracting the same number to both sides of the equation.
3.
Multiply both sides of the equation by the same equation.
4.
Divide both sides of the equation by the same equation.
Examples:
1.
4a + 3 = 3a + 12. Find the value
of a.
Solution
Collecting like terms:
4a
– 3a = 12 – 3
A = 9
NOTE: When collecting like
terms, this always happen (–) minus changes to plus and (+) plus changes to
minus whenever both symbols crosses (=) equals to.
2.
Solve 3(b – 2) = 4(2b – 5)
Solution
Expanding and collecting like terms:
3b
– 6 = 8b – 20 (Expanding in this type of question means multiplying the numbers
in the bracket by the one outside the bracket)
3b
– 8b = -20 + 6
-5b
= -1
Dividing both sides by the co-efficient of b:
b
= -14/-5
=
2 4/5 (2 whole number, 4 all-over 5)
3.
2y + 3 = 3y – 8
Solution
Collecting like terms:
2y
– 3y = -8 – 3
-y
= -11
Dividing both sides by the coefficient of y:
-y/-1 =
-11/-1
y = 11.
NB: Whenever unknown has no
coefficient with it, and there is a negative sign known as minus before it,
automatically the coefficient is 1.
Exercise your brain with the questions below:
1.
4(2m – 5) = 3(2m + 8)
2.
3x + 13 = 1
3.
6x – 2 = 2x + 8
ALO MATHEMATICS
CENTRE implores every one
of us to try and solve the questions above.
We
will be expecting your response.
Thank
You All.