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• [ended]Mathematics Tutoring Session #8 Linear Equation on Thur. 25th Feb 2016 @ 3:00 - 4:00pm

Mathematics

Emmanuel Iwara(Tutor)
25-02-2016 13:01:00 +0000

Good day all

This session has ended for today

The concept of Linear Equation is the most fundamental in mathematics often tested on JAMB and other exams. so lets take a quick look into this topics.

Equation- Is a mathematical statement that shows equality between two expressions.

Linear Equation- Is a mathematical statement that contains only terms in one variable and constant,and the highest power of the variable is 1.

E.g. 4x-3 = 4-2x

Example 1. Solve 4(x-3) = 2(3x -5)

Soln

Expanding and collection of like terms, yield

4x -12 = 6x- 10

= -12 + 10 = 6x - 4x

-2 = 2x

x = -2/2 = -1.

Example 2. Solve the equation x +1 / 5 - 3(x - 1) /10 = 2

Solution

The L.C.M, of 5 and 10 is 10, simplifying will yield

. 2(x +1) - (3x-3) / 10 = 2

Cross - multiplying gives

(2x + 2) - (3x-3) = 10 x 2

2x + 2 - 3x + 3 = 20

collecting like terms

-x + 5 = 20

-x = 20 - 5

-x = 15

x = -15

WORD PROBLEMS

Some statements can be expressed in a mathematical form which will not change the meaning of what is contained in the original statement.

Example 1. A man is five times as old as his son. In five years times he will be thrice as old.What are their ages now?

Solution

Let the son's age be x. Then the father's age will be 5x.

In five years time their age will be,

Son = x + 5.

Father = 5x + 5

But 5x + 5 is thrice x + 5

5x + 5 = 3(x+5)

Expanding and collecting terms

5x + 5 = 3x + 15

2x = 15 - 5

2x = 10

x = 10/2 = 5

Therefore Son age = 5years.

Father age = 5x = 5 x 5 = 25years.

Example 2.Three years ago, a father was twice as old as his son, now, their combined ages amount to 11years.

Find the present age of the father.

Solution

Let father age be x, and the son age be = y

Three years ago, father = x-3, son = y-5

Then x-3 = 2(y-5)

x-3 = 2y - 10

x-2y = -10 + 3

x-2y = -7-------------------------------------(1)

now their combined age will be x + y = 11----------------(2)

Solving simultaneously

(2) - (1)

x + y - x + 2y = 11 -(-7)

3y = 18

y = 18/3 = 6

Putting (y) into equ(2)

x = 11- 6 = 5 = Present Age of the father.

Example 3.When the same number is subtracted from the numerator and denominator of the fraction 18/20, the result is 11/13 ,find the number.

Solution

Let the number be x, then we have

18 - x / 20 - x = 11/13

Cross - multiplying we have

13 (18 - x) = 11 ( 20 - x)

234 -13x = 220 - 11x

Collecting like terms

234 -220 = -11x + 13x

14 = 2x

x = 14/2 = 7

Can anyone try solving the Questions below;

(a) Add the same number to the numerator and denominator of 3/18. If the resulting fraction is 1/2. Jamb Number Question(48), 1978.

(b) Solve 1 / x + 1 - 1 / x+3 = 1/4
Jamb Question Number (20),1981.

(c) Five years ago, a father was 3times as old as his son, now, their combined ages amount to 110 years. thus,the present age of the father is----(Jamb Question Number (13),1978).

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• Oluyemi oladiran

nyc.... keep up d gud work....very understanding

0 25-02-2016 13:10:00 +0000

• Omotayo Olalekan

(b) X = 2.125 or 17/8

0 25-02-2016 13:16:00 +0000

• Omotayo Olalekan

(c) Present Father's age = 87.5 = 87years 5months.

0 25-02-2016 13:24:00 +0000

• Gbokoyi Eniola

(a)..3+x \18+x =1\2

0 25-02-2016 13:30:00 +0000

• Emmanuel Iwara(Tutor)

@Oluyemi thanks you are welcome

0 25-02-2016 14:09:00 +0000

• Emmanuel Iwara(Tutor)

@Omotayo thanks for solving the correct solution will be post after the section is over.

0 25-02-2016 14:12:00 +0000

• Emmanuel Iwara(Tutor)

hello class are we all there, ask Questions if you have any i will try to give solutions to your questions.

0 25-02-2016 14:21:00 +0000

• Emmanuel Iwara(Tutor)

@Gbokoyi thanks for giving a try you would have simplify further. But stay close the correct solution will be post after the section is over.

0 25-02-2016 14:27:00 +0000

• Emmanuel Iwara(Tutor)

@Omotayo are you there please try and solve this. Find the value of x in the given problem 6x +y = 2y +5x.

0 25-02-2016 14:37:00 +0000

• Emmanuel Iwara(Tutor)

@ all can you ask questions on any topic you have problem am waiting

0 25-02-2016 14:41:00 +0000