*Thus, in the equation x 3 = 7, the left-hand member is x 3 and the right-hand member is 7. However, the solutions of most equations are not immediately evident by inspection.*Equations may be true or false, just as word sentences may be true or false. Hence, we need some mathematical "tools" for solving equations.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.

*Thus, in the equation x 3 = 7, the left-hand member is x 3 and the right-hand member is 7. However, the solutions of most equations are not immediately evident by inspection.*

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

Solution Dividing both members by -4 yields In solving equations, we use the above property to produce equivalent equations in which the variable has a coefficient of 1. We first combine like terms to get 5y = 20 Then, dividing each member by 5, we obtain In the next example, we use the addition-subtraction property and the division property to solve an equation. Solution First, we add -x and -7 to each member to get 4x 7 - x - 7 = x - 2 - x - 1 Next, combining like terms yields 3x = -9 Last, we divide each member by 3 to obtain Consider the equation The solution to this equation is 12.

Also, note that if we multiply each member of the equation by 4, we obtain the equations whose solution is also 12.

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. The first-degree equations that we consider in this chapter have at most one solution. Notice in the equation 3x 3 = x 13, the solution 5 is not evident by inspection but in the equation x = 5, the solution 5 is evident by inspection.

Determine if the value 3 is a solution of the equation 4x - 2 = 3x 1 Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. The solutions to many such equations can be determined 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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