- What is algebraic expression
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- What is algebraic equation
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- What is Linear equation in one Variable
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- Solving Equations which have Linear Expressions on one Side and Numbers on the other Side
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- Word Problem
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- Solving Equations having the Variable on both Sides
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- Reducing Equations to Simpler Form
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- Equations Reducible to the Linear Form

10

2

3

2

x

A

An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side.

5

2

11xy+1 =98

x

1)These all above equation contains the equality (=) sign.

2) The above equation can have more than one variable

3) The above equation can have highest power of variable > 1

4) The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS)

5) In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.

6) We assume that the two sides of the equation are balanced. We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. We get the solution after generally performing few steps

a) algebraic equation in one variable

b) variable will have power 1 only

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2

We will focus on Linear equation in One variable in this chapter.

2x -3= 5

3x-11= 22

3x-11= 22

1) Transpose (changing the side of the number) the Numbers to the side where all number are present. We know the sign of the number changes when we transpose it to other side

2) Now you will have a equation have variable on one side and number on other side. Add/subtract on both the side to get single term

3) Now divide or multiply on both the side to get the value of the variable

2x -3= 5

Transposing 3 to other side

2x=5+3

2x=8

Dividing both the sides by 2

x=4

1) First read the problem carefully. Write down the unknown and known

2) Assume one of the unknown to x and find the other unknown in term of that

3) Create the linear equation based on the condition given

4) Solve them by using the above method

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

The unknown are length and breadth.

Let the breadth be x m.

Then as per question the length will be (2x + 2) m.

Perimeter of swimming pool = 2(l + b) = 154 m

2(2x + 2 + x) = 154

2(3x + 2) = 154

Dividing both sides by 2

3x + 2 = 77

Transposing 2 to R.H.S, we obtain

3x = 77 − 2

3x = 75

Dividing 3 on both the sides

x = 25

So

Breath is 25 m

Length =2x + 2 = 2 × 25 + 2 = 52m

Hence, the breadth and length of the pool are 25 m and 52 m respectively.

2x -3= 6-x

3x-11= 4x

1) Here we Transpose (changing the side of the number) both the variable and Numbers to the side so that one side contains only the number and other side contains only the variable. We know the sign of the number changes when we transpose it to other side.Same is the case with Variable

2) Now you will have a equation have variable on one side and number on other side. Add/subtract on both the side to get single term

3) Now divide or multiply on both the side to get the value of the variable

2x -3= 6-x

Transposing 3 to RHS and x to LHS

2x+x=6+3

3x=9

Dividing both the sides by 3

x=3

1) Take the LCM of the denominator of both the LHS and RHS

2) Multiple the LCM on both the sides, this will reduce the number without denominator and we can solve using the method described above

Solve the linear equation

L.C.M. of the denominators, 2, 3, 4, and 5, is 60.

So Multiplying both sides by 60, we obtain

30

Transposing 20x to R.H.S and 12 to L.H.S, we obtain

30

10

Dividing both the sides by 10

x=87/10=8.7

The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

Let the common ratio between their ages be

According to the situation given in the question,

Multiplying both the sides by (7x+4)

(5x+4) =3(7x+4)/4

or

20x+16=21x+12

Transposing 20x to RHS and 12 to LHS

4=x

x=4

Hari’s age = 5

Harry’s age = 7

Therefore, Hari’s age and Harry’s age are 20 years and 28 years respectively.

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