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This imagery suggests several ways to solve the equation, which is to find the value of x.
Let us think of it as a final step where “x” is on the LHS and a number comes on the RHS. The obviously the solution of the equation is that x has a value equal to that particular number. But how do we arrive at the final step?
The imagery again suggests that the balance is at equilibrium. It also suggests that the equilibrium would not be disturbed if the “same thing” is done to both sides of the equation. What are some of the “same things” that can be done to both sides?
The equilibrium would not be disturbed if
The same weight is added to both the pans
The same weight is taken away from both the pans
The items on both sides are doubled or trebled or halved
Mathematically the above steps are equal to adding, subtracting, multiplying, dividing both the sides by the same number.
We need to strategise and do the above steps in such a way that in the last step only the variable is left on the LHS and a number on the RHS. Let us see how to do this with the example of the same equation.
The meaning of the solution is that 68 degrees on the Fahrenheit scale is equal to 20 degrees on the Centigrade scale.
Equations in Real Life
Many simple events in life, which feature a quantity which needs to be found, can be cast in terms of an equation and a solution arrived at.
One of the major objectives of science is to cast hypotheses in terms of equations or formulas. Most real life situations have multiple variables and could be connected by complex mathematical operators. One of the major efforts is to find out procedures for solving different kinds of equations.
One easily understandable use of equations is working out the monthly loan repayment when we take a loan to purchase a car. The variables in this situation can be – the value of the car, the repayment period, the rate of interest of the loan etc.
Even for solving complex equations, the strategy in essence is the same as the above, though the details of the kind of numerical & operational manipulations may be different.
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