How To Solve A Calculus Problem

How To Solve A Calculus Problem-35
For example, the stated problem "Find a number which, when added to 3, yields 7" may be written as: 3 ?

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Consider the equation 3x = 12 The solution to this equation is 4.

Also, note that if we divide each member of the equation by 3, we obtain the equations whose solution is also 4.

Equations such as x 3 = 7 are first-degree equations, since the variable has an exponent of 1.

The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. In Section 3.1 we solved some simple first-degree equations by inspection.

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.

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.

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.


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