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Simple Equations

    What Have We Discussed ?

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7th class > Simple Equations > What Have We Discussed ?

What Have We Discussed ?

1.Definition and Solution of an Equation: An equation is a condition on a variable such that two expressions in the variable should have equal value. The value of the variable for which the equation is satisfied is called the of the equation.

2.Maintaining Balance in Equations: An equation if the LHS and the RHS are interchanged.

In the case of the balanced equation, the value of the LHS remains equal to the value of the RHS, if we :

(i) add the number to both the sides (or)

(ii) subtract the number from both the sides (or)

(iii) multiply both sides by the number (or)

(iv) divide both sides by the number, the balance remains undisturbed.

3.Methodology for Solving Equations: It is a systematic approach to finding the value of the variable that satisfies the equation. This process typically involves a series of mathematical operations applied identically to both sides of the equation. The goal is to the variable on one side, thereby determining its value.

Here's a breakdown of the general steps involved in this methodology:

(i)Identify the Equation: Start by clearly identifying the equation you need to solve. An equation will have an sign ('=') separating two expressions.

(ii)Simplify Both Sides: If necessary, simplify each side of the equation. This might include expanding brackets, combining like terms (or) simplifying fractions.

(iii)Isolate the Variable: Use algebraic operations to get the variable you are solving for on one side of the equation. This often involves:

Transposing Terms: Move terms from one side of the equation to the other. Remember, when you transpose a term, its operation .

i.e. addition becomes subtraction and vice versa; multiplication becomes division and vice versa. For example, transposing +3 from the LHS to the RHS in the equation x + 3 = 8 gives x = 8 – 3 = .

Balancing Operations: Perform the same operation on both sides of the equation to maintain balance. This includes adding, subtracting, multiplying, or dividing both sides by the same value.

(iv)Solve for the Variable: Once the is isolated, perform any necessary arithmetic to solve for its value.

(v)Check Your Solution: Substitute the solution back into the original equation to verify that it satisfies the equation.

(vi)State the Solution: Clearly state the value of the variable that solves the .

4.Building Equations from Solutions and Practical Applications: We also learned how, using the technique of doing the same mathematical operation (for example, adding the same number) on both sides, we could build an equation starting from its solution. Further, we also learned that we could relate a given equation to some appropriate practical situation and build a practical word problem/puzzle from the equation.