In class 7 Maths Chapter 4 notes, the various methods to solve an equation maintaining the equality of the expression along with the transposition methods are discussed.
What is an Equation?
An equation, also known as the algebraic equation, is a condition on a variable such that two expressions in the variable have equal value. A variable’s value is not fixed, it takes the value of different numerical values. An equation has an equality sign. The equality sign proves that the value of the expression to the left-hand side or LHS is equal to the value of the expression to the right-hand side or RHS. An equation remains the same, even when the L.H.S and R.H.S of the equation are interchanged.
Solving an Equation
In case of a balanced equation, when both the sides are
- added by the same number
- subtracted by the same number
- multiplied by the same number
- divided by the same number
the balance between the two equations remains undisturbed, in other words, the value of L.H.S remains equal to the R.H.S.
- a) Subtracting the same number on both the sides
Example: Consider an equation,x+4=8,
(i) Let us subtract 4 from both the sides of the equation, now the new LHS and RHS obtained are
New LHS=x+4-4=x, and New RHS=8-4=4
New LHS=New RHS, x=4
The equality of the equation is retained and the balance is not disturbed. Now to confirm, substitute x=4, in the original equation,
x+4=8=4+4=8
- b) Adding the same number on both the sides
(ii) Now let us consider another equation, x-5=4, let us add 5 to both the sides, the
newly obtained L.H.S and R.H.S are given below:
New LHS=,x-5+5=x,and New RHS= 4+5=9
New LHS=New RHS, x=9
The equality of the equation is retained and the balance is not disturbed. Now to confirm, substitute x=9, in the original equation,
x-5=4=9-5=4
- c) Multiplying and Dividing the same number on both the sides
(iii) Similarly, for multiplication and division, let us consider the equations
\(6y=24\) —– (1) \(\frac{m}{4}=8\) —– (2)Now, divide both the sides of equation (1) by 6, the newly obtained L.H.S and R.H.S
are:
New L.H.S =\(\frac{6y}{y}=6\) and the New R.H.S =\(\frac{24}{6}=4\)
New LHS = New RHS, y=4
The equality is retained in the balanced equation. Substituting y=4, in the original
equation we get
\(6y=24=6\times 4=24\)Now multiplying both sides of equation (2) by 4, we get the new L.H.S and R.H.S as
New L.H.S = \(\frac{m}{4}\times 4=m\) and New R.H.S = \(8\times 4=32\)
New LHS=New RHS, m=32
The equality is retained in the balanced equation. Substituting m=32, in the original
equation we get
\(\frac{m}{4}=\frac{32}{4}=8\)
Transposing
The meaning of transpose is to move from one side to another. Transposition of a number has the same effect as adding or subtracting the same number from both the sides of the equation. While transposing a number from one side to another, the sign of the number is changed. Let us take a look at the below example, to better understand transposing.
Example: Consider the equation x+6=12, transposing 6 from the L.H.S to the R.H.S gives us the value of x as follows
x=12-6=6
Simple Equations Class 7 Maths Important Questions
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