Example 2 Find the solution of each equation by inspection.

Solution We can solve for t by substituting 24 for d and 3 for r. Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful.

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. 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.

Also, note that if we multiply each member of the equation by 4, we obtain the equations whose solution is also If both members of an equation are divided by the same nonzero quantity, the resulting equation is equivalent to the original equation.

For example, the stated problem "Find a number which, when added to 3, yields 7" may be written as: If both members of an equation are multiplied by the same nonzero quantity, the resulting equation Is equivalent to the original equation.

It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.

You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require. 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. Combine like terms in each member of an equation. Sometimes, it is necessary to apply more than one such property. Use the division property to obtain a coefficient of 1 for the variable.

Example 1 Write an equivalent equation to by multiplying each member by 6. Also, note that if we divide each member of the equation by 3, we obtain the equations whose solution is also 4. In general, we have the following property, which is sometimes called the multiplication property.

The equations section lets you solve an equation or system of equations. The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

The algebra section allows you to expand, factor or simplify virtually any expression you choose.

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. The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation.

We use the same methods demonstrated in the preceding sections. The graphs section contains commands for plotting equations and inequalities. The following property, sometimes called the addition-subtraction property, is one way that we can generate equivalent equations.

Solution We can solve for x by first adding -b to each member to get then dividing each member by a, we have. The value of the variable for which the equation is true 4 in this example is called the solution of the equation.

If the same quantity is added to or subtracted from both members of an equation, the resulting equation is equivalent to the original equation. Any one or more of the following steps listed on page may be appropriate. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted.

We substitute the known values in the formula and solve for the unknown variable by the methods we used in the preceding sections. Send What can QuickMath do?

The inequalities section lets you solve an inequality or a system of inequalities for a single variable. The matrices section contains commands for the arithmetic manipulation of matrices.Solving Algebra word problems is useful in helping you to solve earthly problems.

While the 5 steps of Algebra problem solving are listed below, this article will focus on the first step, Identify the problem. Hence, we need some mathematical "tools" for solving equations. EQUIVALENT EQUATIONS. Equivalent equations are equations that have identical solutions.

Thus, 3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5. are equivalent equations, because 5 is the only solution of each of them.

The ideas below, which provide you with general steps or strategies to solve math problems, are similar to those expressed in Pólya’s book and should help you untangle even the most complicated math problem. Webmath is a math-help web site that generates answers to specific math questions and problems, as entered by a user, at any particular moment.

The math answers are generated and displayed real-time, at the moment a web user types in their math problem and clicks "solve.". Step-by-Step Calculator Solve problems from Pre Algebra to Calculus step-by-step. Part of Technical Math For Dummies Cheat Sheet.

Word problems aren’t just on school tests.

You solve word problems every day in your work or even while you’re just out and about. Don’t worry — these steps make solving word problems easier than you think. Just follow these easy steps to take away the mystery: Read the problem.

DownloadSolving math problems with steps

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