Notice that since we are dividing by a negative number, we must change the direction of the inequality. To obtain x on the left side we must divide each term by - 2. The last statement, - a > -x, can be rewritten as - x a, then - x 3 then -5 6 Remember, adding the same quantity to both sides of an inequality does not change its direction. Now add - x to both sides by the addition rule. This graph represents every real number greater than -5.Д®xample 8 Make a number line graph showing that x > - 1 and x - 1 and x 4 indicates the number 4 and all real numbers to the right of 4 on the number line.

This graph represents every real number greater than 4.Д®xample 7 Graph x > -5 on the number line. We usually read the symbol as 'greater than.' For instance, a > b is read as 'a is greater than b.' Notice that we have stated that we usually read a 3.Д®xample 3 4 > - 2, because 4 is to the right of -2 on the number line. The symbols are inequality symbols or order relations and are used to show the relative sizes of the values of two 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. The set composed of rational and irrational numbers is called the real numbers. This set includes such numbers as and so on. There is also a set of numbers, called the irrational numbers, that cannot be expressed as the ratio of integers. We have already discussed the set of rational numbers as those that can be expressed as a ratio of two integers.

Use the inequality symbol to represent the relative positions of two numbers on the number line.

We can rewrite the answer another way if we wish. Notice in this example that r was left on the right side and thus the computation was simpler. Find the yearly rate when the amount of interest, the principal, and the number of days are all known. We must multiply each term inside the parentheses by the factor preceding the parentheses.Д¬hanging 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.Д®xample 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. Removing parentheses does not mean to merely erase them. Solve for c.ДЄ trapezoid has two parallel sides and two nonparallel sides. The most commonly used literal expressions are formulas from geometry, physics, business, electronics, and so forth.Д®xample 4 is the formula for the area of a trapezoid. Multiplying numerator and denominator of a fraction by the same number is a use of the fundamental principle of fractions. The advantage of this last expression over the first is that there are not so many negative signs in the answer. 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 Sometimes the form of an answer can be changed. Compare the solution with that obtained in the example. Solve the equation 2x + 2y - 9x + 9a by first subtracting 2.v from both sides. We divide by the coefficient of x, which in this case is ab. The step-by-step procedure discussed and used in chapter 2 is still valid after any grouping symbols are removed.Д®xample 1 Solve for c: 3(x + c) - 4y = 2x - 5cДЄt 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.

It is occasionally necessary to solve such an equation for one of the letters in terms of the others. Apply previously learned rules to solve literal equations.ДЄn equation having more than one letter is sometimes called a literal equation.Upon completing this section you should be able to: Then follow the procedure learned in chapter 2.

Would be to first subtract 3x from both sides obtainingДЇirst remove parentheses. Using the same procedures learned in chapter 2, we subtract 5 from each side of the equation obtainingД®xample 2 Solve for x and check: - 3x = 12 Upon completing this section you should be able to solve equations involving signed numbers.Д®xample 1 Solve for x and check: x + 5 = 3 SOLVING EQUATIONS INVOLVING SIGNED NUMBERS OBJECTIVES We will also study techniques for solving and graphing inequalities having one unknown. Now that we have learned the operations on signed numbers, we will use those same rules to solve equations that involve negative numbers. In chapter 2 we established rules for solving equations using the numbers of arithmetic. Equations and Inequalities Involving Signed Numbers

Solve 0.3 times 10