The value of the variable for which the equation is true 4 in this example is called the solution of the equation. We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member.
The first-degree equations that we consider in this chapter have at most one solution. The solutions to many such equations can be determined by inspection. However, the solutions of most equations are not immediately evident by inspection.
Hence, we need some mathematical "tools" for solving equations. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted. The following property, sometimes called the addition-subtraction property , is one way that we can generate equivalent equations. If the same quantity is added to or subtracted from both members of an equation, the resulting equation is equivalent to the original equation.
The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation. 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 -1 to or subtract 1 from each member, we get. In the above example, we can check the solution by substituting - 3 for x in the original equation. The symmetric property of equality is also helpful in the solution of equations. This enables us to interchange the members of an equation whenever we please without having to be concerned with any changes of sign. There may be several different ways to apply the addition property above.
Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful. Compare the volume and surface area of the Are you sure you want to delete this answer? Check with other answers i am not a mathlete. You can even type it into a graphing calculator. D X must be greater than Zero. You would need to know how thick the shell is. I guess you could approximate the volume with a hemisphere? Have a question the night before a test? Log on and connect to an expert math tutor.
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