Domanda del libro di testo
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 43
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. 1 - x/2 > 4
Guida verificata passo dopo passo1
Start with the given inequality: \(1 - \frac{x}{2} > 4\).
Isolate the term containing \(x\) by subtracting 1 from both sides: \(1 - \frac{x}{2} - 1 > 4 - 1\), which simplifies to \(- \frac{x}{2} > 3\).
To solve for \(x\), multiply both sides of the inequality by \(-2\) to eliminate the fraction. Remember, when multiplying or dividing an inequality by a negative number, you must reverse the inequality sign: \(x < -6\).
Express the solution in interval notation. Since \(x\) is less than \(-6\), the solution set is \((-\infty, -6)\).
To graph the solution on a number line, draw a number line, mark the point \(-6\) with an open circle (because \(x\) is strictly less than \(-6\), not equal), and shade all values to the left of \(-6\).
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Solving Linear Inequalities
Linear inequalities involve expressions with variables raised to the first power and inequality signs (>, <, ≥, ≤). To solve them, isolate the variable on one side by performing inverse operations, similar to solving linear equations, but pay attention to inequality rules.
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Percorso guidato
06:07
Linear Inequalities
Effect of Multiplying or Dividing by Negative Numbers
When solving inequalities, multiplying or dividing both sides by a negative number reverses the inequality sign. This rule is crucial to maintain the inequality's truth and must be applied carefully during the solution process.
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Percorso guidato
04:22Dividing Complex Numbers
Interval Notation and Number Line Graphing
Interval notation expresses solution sets using parentheses and brackets to indicate open or closed intervals. Graphing on a number line visually represents these solutions, showing which values satisfy the inequality and whether endpoints are included.
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05:18Interval Notation
Pratica correlata
Domanda del libro di testo
In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)2
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Domanda del libro di testo
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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Domanda del libro di testo
Solve each equation in Exercises 41–60 by making an appropriate substitution.
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Domanda del libro di testo
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 - 3/2 ≤ x/2 + 1
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Domanda del libro di testo
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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