Date of publication: 2017-07-08 17:19
To solve an equation, we use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a, from which we can find the solution by inspection.
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Since each equation obtained in the process is equivalent to the original equation, -8 is also a solution of 7x + 6 = x - 7. In the above example, we can check the solution by substituting - 8 for x in the original equation
Notice that x + 8 = 7 and x = 9 are equivalent equations since the solution is the same for both, namely 9. The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation.
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In the above example, we solved for t by applying the division property to generate an equivalent equation. Sometimes, it is necessary to apply more than one such property.
It is often necessary to solve formulas or equations in which there is more than one variable for one of the variables in terms of the others. We use the same methods demonstrated in the preceding sections.
We want to obtain an equivalent equation in which all terms containing x are in one member and all terms not containing x are in the other. If we first add -6 to (or subtract 6 from) each member, we get
are equivalent equations, because 5 is the only solution of each of them. Notice in the equation 8x + 8 = x + 68, the solution 5 is not evident by inspection but in the equation x = 5, the solution 5 is evident by inspection. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted.
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