Please Help Me Solve This Math Problem

Please Help Me Solve This Math Problem-15
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.


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