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Additional resources for Colleges That Create Futures: 50 Schools That Launch Careers By Going Beyond the Classroom (College Admissions Guides)
First, you have whole numbers. Whole numbers are also called “counting numbers” and include 0, 1, 2, 3, 4, 5, 6, . . You see the pattern here. 30 Express Review Guides: ALGEBRA II Next on the roster are integers. Integers are all positive and negative whole numbers including zero: –3, –2, –1, 0, 1, 2, 3, . . Rational numbers, good old rational numbers. 666. ). And rounding out the team are irrational numbers. Irrational numbers cannot be expressed as terminating or repeating decimals. Some examples: or ͙2ෆ.
CHECKING EQUATIONS After you solve an equation, you can check your answer by substituting your value for the variable into the original equation. Algebra Boot Camp Example We found that the solution for 7x – 11 = 29 – 3x is x = 4. To check that the solution is correct, substitute 4 for x in the equation: 7x – 11 = 29 – 3x 7(4) – 11 = 29 – 3(4) 28 – 11 = 29 – 12 17 = 17 This equation is true, so x = 4 is the correct solution! INSIDE TRACK SPECIAL TIPS FOR CHECKING EQUATIONS ON EXAMS IF TIME PERMITS, check all equations.
You can check your answer at the end of this chapter. 3. If 8a + 16b = 32, what does a equal in terms of b? INEQUALITIES An inequality is two numbers or expressions that are connected with an inequality symbol. Inequalities contain the greater than, less than, greater than or equal to, less than or equal, or not equal to symbols. When you solve the inequalities for x, you can figure out a range of numbers that your unknown is allowed to be. This symbol . . Means . . > “Greater than” Ն “Greater than or equal to” < “Less than” Յ “Less than or equal to” ≠ “Not equal to” Algebra Boot Camp Here are some examples of inequalities: 2<5 9>3 4Յ4 2x + 5 11 (2 is less than 5) (9 is greater than 3) (4 is less than or equal to 4) (2x added to 5 is not equal to 11) Now, there is one rule that you need to remember when dealing with inequalities: When you multiply or divide by a negative number, you need to reverse the sign.