184 Chapter 2 Linear Equations and Inequalities in One Variable SECTION 2.2 The Addition Property of Equality 4. A linear equation in one variable is an equation that can be written in the form . An example of a linear equation in one variable is . 5. To solve a linear equation in one variable, the goal is to produce an equation of the form or . 6. equations are equations with the same solution set. 7. The addition property of equality states that we can or the same number from both sides of an equation and not change the solution set. 8. To solve an equation, we must each side as much as possible. Then we must isolate the to one side and the to the other. SECTION 2.3 The Multiplication Property of Equality 9. The multiplication property of equality enables us to or both sides of an equation by the same number. 10. If the coefficient of the variable is a fraction, we can multiply both sides of the equation by its to obtain a coefficient of 1 on the variable. 11. integers are integers that follow one another. An example of consecutive integers is , an example of consecutive odd integers is , and an example of consecutive even integers is . If x is an integer, then and represents the next two consecutive integers. SECTION 2.4 More on Solving Linear Equations 12. To solve equations with fractions, we can multiply both sides of the equation by the to obtain an equivalent equation without fractions. 13. To solve equations with decimals, we can multiply both sides of the equation by the that eliminates the decimals. 14. A(n) equation is an equation that is true for some values of the variable but not true for others. 15. A(n) is an equation that is not true for any values of the variable. The solution set for these equations is . 16. A(n) is an equation that is true for all values of the variable. The solution set for these equations is . SECTION 2.5 Formulas and Applications from Geometry 17. A(n) is an equation that expresses the relationship between two or more variables. 18. To evaluate a formula, we the given values in place of the variable and simplify. 19. The perimeter of a polygon is the around the figure. 20. The distance around a circle is its . 21. The of a figure is the number of square units it takes to cover the inside of the figure. 22. The sum of the measures of complementary angles is . The sum of the measures of supplementary angles is . 23. A right angle has measure and a angle has measure of 180°. 24. If x represents the measure of an angle, represents the measure of its complement and represents the measure of its supplement. 25. Vertical angles, or angles, are formed by intersecting lines. These angles are in measure. 26. The sum of the measures of the angles in a triangle is . SECTION 2.6 Percent, Rate, and Mixture Problems 27. Percent means . So, 30% = = . 28. is the amount of money collected for using or borrowing money. The is I = Prt. 29. When working with mixture problems, we must find the amount of substance in each solution. We do this by multiplying the strength of the solution by the of the solution. 30. To find the value of a collection of coins, multiply the number of coins by the of each coin. 31. Distance traveled is the multiplied by the traveled. In symbols, d = . SECTION 2.7 Linear Inequalities in One Variable 32. A linear inequality in one variable is an inequality of the form . 33. A(n) of a linear inequality is a value that makes the inequality true. 34. The picture of the solution set of an inequality is the of the solution set. 35. If an endpoint of a solution set of an inequality is included in the solution, a is used. If an endpoint of a solution set is not included in the solution set, a is used. 36. A concise way to express the solution set of an inequality is . 37. The symbol indicates that the solution of an inequality continues to the right indefinitely. The symbol indicates that the solution of an inequality continues indefinitely to the left. A is always used with these notations. 38. The notation is also used to represent the solution set of an inequality. This notation states the conditions the solution must satisfy. 39. When solving linear inequalities, we can or the same number from both sides of an inequality and not change the relationship between the two expressions.
hendricks_beginning_algebra_1e_ch1_3
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