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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 45
Capitolo 2, Problema 45

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. (x - 4)/6 ≥ (x - 2)/9 + 5/18

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Start by writing down the inequality: \(\frac{(x - 4)}{6} \geq \frac{(x - 2)}{9} + \frac{5}{18}\).
To eliminate the fractions, find the least common denominator (LCD) of 6, 9, and 18, which is 18. Multiply every term on both sides of the inequality by 18 to clear the denominators.
After multiplying, simplify each term: \(18 \times \frac{(x - 4)}{6} = 3(x - 4)\), \(18 \times \frac{(x - 2)}{9} = 2(x - 2)\), and \(18 \times \frac{5}{18} = 5\).
Rewrite the inequality without fractions: \(3(x - 4) \geq 2(x - 2) + 5\). Then, distribute the constants inside the parentheses: \(3x - 12 \geq 2x - 4 + 5\).
Combine like terms on the right side: \(2x - 4 + 5 = 2x + 1\). Now, solve the inequality \(3x - 12 \geq 2x + 1\) by isolating \(x\) on one side.

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Solving Linear Inequalities

Linear inequalities involve expressions with variables raised to the first power and inequality symbols (>, <, ≥, ≤). Solving them requires isolating the variable on one side while maintaining the inequality's direction, often by performing algebraic operations like addition, subtraction, multiplication, or division.
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Linear Inequalities

Manipulating Fractions in Inequalities

When solving inequalities with fractions, it is important to find a common denominator or clear fractions by multiplying both sides by the least common denominator. Care must be taken when multiplying or dividing by negative numbers, as this reverses the inequality sign.
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Linear Inequalities with Fractions & Variables on Both Sides

Interval Notation and Graphing Solutions

Interval notation expresses solution sets as intervals on the number line, using parentheses for strict inequalities and brackets for inclusive inequalities. Graphing these solutions involves shading the appropriate region on a number line and indicating boundary points as open or closed dots based on the inequality.
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Interval Notation
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Domanda del libro di testo

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 5/2x - 8/9 = 1/18 - 1/3x

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Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

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Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

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In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 8 + √-32)/24

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