Section 2.4 Linear Inequalities and Applications 85 91. y - y1 = m(x - x1) for x 92. A = h(b1 + b2) 2 for b1 You Be the Teacher! Correct each student’s errors, if any. 93. Agnes invests $4500 in two accounts. The amount she invests in the second account is $300 less than twice the amount invested in the first account. How much does Agnes invest in the first account? Jada’s work: Let x be the amount invested in the first account and 2x be the amount invested in the second account. x + 2x = 4500 3x = 4500 x = 1500 94. Solve the formula S = a 1 - r for the variable r. Maureen’s work: S = a 1 - r S(1 - r) = a S - r = a -r = a - S r = a + S Calculate It! The formula A = 100(1.01)4t specifi es the amount A in an account after t yr when $100 is invested at 4% annual interest rate compounded quarterly. Use a graphing calculator to determine the number of years it will take for the account to grow to the given amounts. Round to the nearest year. 95. $150 96. $200 97. $700 98. $1000 SECTION 2.4 Linear Inequalities and Applications Susan uses a phone service provided by a high-speed Internet connection. The service offers a basic residential calling plan for $14.99 for the first 500 min of local and long distance calling plus 3.9¢ for each additional minute. The monthly cost of Susan’s phone bill is represented by 14.99 + 0.039x, where x is the number of additional minutes. How many minutes of calling can Susan use for her cost to be at most $20.00 per month? To answer this question, we must solve a special type of inequality. In this section, we will learn how to solve linear inequalities and their applications. Solutions of Inequalities Until now, we have solved only linear equations in one variable. We now turn our focus to solving linear inequalities in one variable. An inequality is a statement that two quantities are not equal. The following symbols are used to denote inequalities. p < q p is less than q. p ≤ q p is less than or equal to q. p > q p is greater than q. p ≥ q p is greater than or equal to q. A linear inequality is the same as a linear equation except the equality sign is replaced with an inequality symbol. Definition: A linear inequality in one variable is an inequality of the form ax + b < c, where a, b, and c are real numbers and a ≠ 0. Note: The definition of a linear inequality in one variable also applies to inequalities containing the symbols ≤, >, or ≥. ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Graph the solution set of an inequality and write its solution set in interval notation and set-builder notation. 2. Solve a linear inequality using the addition and multiplication properties of inequalities. 3. Solve applications of linear inequalities. 4. Troubleshoot common errors. Objective 1 ▶ Graph the solution set of an inequality and write its solution set in interval notation and set-builder notation.
hendricks_intermediate_algebra_1e_ch1_3
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