Lessons on Introduction to Simple Equations

simple equations

Variables and Expressions​

Variable is a quantity that can take any value, its value is not fixed. It is a symbol for a number whose value is unknown yet.

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Expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables.

Example: 6x – 3 is an expression in variable x.​

Solving an Equation​

​Solving an equation involves performing the same operations on the expressions on either side of the “=” sign so that the value of the variable is found without disturbing the balance.

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​​Methods of Solving an Equation

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Method 1: performing the same operations on the expressions on either side of the “=” sign so that the value of the variable is found without disturbing the balance. Opertions involve Adding, subtracting, multipling or dividing on both sides.

Example: x+2=6 Subtract 2 from LHS and RHS ⇒ LHS: x+2−2=x ⇒ RHS: 6−2=4 But LHS = RHS

​x=4

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​Method 2: Transposing

It involves moving the terms to one side of the equation to find out the value of the variable.​​​​​​​When terms move from one side to another they change their sign.Example: x+2=6Transpose (+2) from LHS to RHS⇒x=6−2⇒x=4

​​Forming Equation from Solution

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Given a solution, many equations can be constructed.

Example:  Given solution: x = 3 Multiply both sides by 4, ⇒ 4x=4×3 Add -5 to both sides, ⇒ 4x−5=12−5 ⇒ 4x−5=7 Similarly, more equations can be constructed.

Applications (Word problem)

Example: Ram’s father is 3 times as old as his son Ram. After 15 years, he will be twice the age of his son. Form an equation and solve it. Solution: Let Ram’s age be x. ⇒ His father’s age is 3x. After 15 years: 3x+15=2(x+15) On solving, 3x+15=2x+30 3x−2x=30−15 x=15 ∴ Ram’s age is 15 and his dad’s age is 45.

​NOW LET US TEST YOU

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Multiple Choice

x + 3 = 0

x = -3

(is this situation satisfied)

• no

• the question is wrong

• yes

• none of the above

Fill in the Blanks

Write equations for the following statements:

The sum of numbers x and 4 is 9.

Open Ended

Set up an equation in the following cases:

Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)

thank you ​

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