 In symbols, a - b, a c = b c, and a - c = b - c are equivalent equations.Write an equation equivalent to x 3 = 7 by subtracting 3 from each member.The following property, sometimes called the addition-subtraction property, is one way that we can generate equivalent equations.

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For example, the stated problem "Find a number which, when added to 3, yields 7" may be written as: 3 ?

= 7, 3 n = 7, 3 x = 1 and so on, where the symbols ? We call such shorthand versions of stated problems equations, or symbolic sentences.

Since each equation obtained in the process is equivalent to the original equation, -3 is also a solution of 2x 1 = x - 2.

In the above example, we can check the solution by substituting - 3 for x in the original equation 2(-3) 1 = (-3) - 2 -5 = -5 The symmetric property of equality is also helpful in the solution of equations.

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In this case, we get 2x-2x 9 = 3x- 9-2x 9 9 = x from which the solution 9 is obvious.

If we wish, we can write the last equation as x = 9 by the symmetric property of equality.

If we first add -1 to (or subtract 1 from) each member, we get 2x 1- 1 = x - 2- 1 2x = x - 3 If we now add -x to (or subtract x from) each member, we get 2x-x = x - 3 - x x = -3 where the solution -3 is obvious.

The solution of the original equation is the number -3; however, the answer is often displayed in the form of the equation x = -3.

As an arithmetic problem which you said this is, this may be intended to teach you to check your is natural at first to just divide 111,000 by 3000 and get 37, then think because it came out so nicely, it must be right!…

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