The Bachelor of Fine Arts B. The College also awards the Bachelor of Music B.

Equations and Inequalities Involving Signed Numbers In chapter 2 we established rules for solving equations using the numbers of arithmetic. Now that we have learned the operations on signed numbers, we will use those same rules to solve equations that involve negative numbers.

We will also study techniques for solving and graphing inequalities having one unknown. Example 1 Solve for x and check: Then follow the procedure learned in chapter 2.

Identify a literal equation. Apply previously learned rules to solve literal equations. An equation having more than one letter is sometimes called a literal equation.

It is occasionally necessary to solve such an equation for one of the letters in terms of the others. The step-by-step procedure discussed and used in chapter 2 is still valid after any grouping symbols are removed. Example 1 Solve for c: At this point we note that since we are solving for c, we want to obtain c on one side and all other terms on the other side of the equation.

Thus we obtain Remember, abx is the same as 1abx. We divide by the coefficient of x, which in this case is ab. Compare the solution with that obtained in the example. Sometimes the form of an answer can be changed. In this example we could multiply both numerator and denominator of the answer by - l this does not change the value of the answer and obtain The advantage of this last expression over the first is that there are not so many negative signs in the answer.

Multiplying numerator and denominator of a fraction by the same number is a use of the fundamental principle of fractions. The most commonly used literal expressions are formulas from geometry, physics, business, electronics, and so forth. Example 4 is the formula for the area of a trapezoid.

A trapezoid has two parallel sides and two nonparallel sides. The parallel sides are called bases. Removing parentheses does not mean to merely erase them.

We must multiply each term inside the parentheses by the factor preceding the parentheses. Changing the form of an answer is not necessary, but you should be able to recognize when you have a correct answer even though the form is not the same.

Example 5 is a formula giving interest I earned for a period of D days when the principal p and the yearly rate r are known. Find the yearly rate when the amount of interest, the principal, and the number of days are all known. Solution The problem requires solving for r. Notice in this example that r was left on the right side and thus the computation was simpler.

We can rewrite the answer another way if we wish. Use the inequality symbol to represent the relative positions of two numbers on the number line. Graph inequalities on the number line.

We have already discussed the set of rational numbers as those that can be expressed as a ratio of two integers. There is also a set of numbers, called the irrational numbers, that cannot be expressed as the ratio of integers. This set includes such numbers as and so on.

The set composed of rational and irrational numbers is called the real numbers.

Given any two real numbers a and b, it is always possible to state that Many times we are only interested in whether or not two numbers are equal, but there are situations where we also wish to represent the relative size of numbers that are not equal.If the same quantity is added to each side of an inequality, the results are unequal in the same order.

Example 1 If 5 8, then 5 + 2 8 + 2. Example 2 If 7 10, then 7 - 3 10 - 3. Contact HBO Customer Service. Find HBO Customer Support, Phone Number, Email Address, Customer Care Returns Fax, Number, Chat and HBO FAQ.

Speak with Customer Service, Call Tech Support, Get Online Help for Account Login. Urbanism, Architecture, and the Use of Space Nepal historically was one of the least urbanized countries in the world, but urbanization is accelerating, especially in the capital, and urban sprawl and pollution have become serious problems.

corresponding remote interior angles. Write two inequalities to express the relationships among the measures of the angles of ABC. $(5 Solve each inequality. Graph the solution set on a number line.

$(5 $(5 $(5 $(5 $(5 $(5 $(5 $(5 Write an algebraic expression to represent each verbal expression. This course introduces students to the fundamental principles that govern fashion. The history of fashion trends is examined prior to a discussion on product development issues, distribution, pricing, and .

Who gets to be where? The Arsenal of Exclusion & Inclusion examines some of the policies, practices, and physical artifacts that have been used by planners, policymakers, developers, real estate brokers, community activists, and other urban actors in the United States to draw, erase, or .

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