Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. -2x² + 4x + 3 = 0
72
views
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema R.6.89
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. 4x + 7 ———— ≤ 2x + 5 -3
Guida verificata passo dopo passo1
Start by rewriting the inequality clearly: \(\frac{4x + 7}{-3} \leq 2x + 5\).
Multiply both sides of the inequality by \(-3\) to eliminate the denominator. Remember, multiplying by a negative number reverses the inequality sign, so the inequality becomes: \(4x + 7 \geq -3(2x + 5)\).
Distribute the \(-3\) on the right side: \(4x + 7 \geq -6x - 15\).
Collect like terms by adding \$6x$ to both sides and subtracting \(7\) from both sides: \(4x + 6x \geq -15 - 7\), which simplifies to \(10x \geq -22\).
Finally, divide both sides by \(10\) (a positive number, so the inequality sign stays the same): \(x \geq \frac{-22}{10}\). Express the solution set in interval notation as \([\frac{-22}{10}, \infty)\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Solving Rational Inequalities
Rational inequalities involve expressions with variables in the numerator and denominator. To solve them, first bring all terms to one side to form a single rational expression, then determine where the expression is positive or negative by analyzing critical points from the numerator and denominator.
Video consigliato:
Percorso guidato
2:58
Rationalizing Denominators
Critical Points and Sign Analysis
Critical points occur where the numerator or denominator equals zero, dividing the number line into intervals. By testing values in each interval, you can determine the sign of the rational expression, which helps identify where the inequality holds true.
Video consigliato:
Percorso guidato
6:58Convert Points from Rectangular to Polar
Interval Notation and Domain Restrictions
Interval notation expresses solution sets compactly using parentheses and brackets. When solving inequalities with denominators, exclude values that make the denominator zero, as these are not in the domain, ensuring the solution set respects these restrictions.
Video consigliato:
Percorso guidato
06:01i & j Notation
Pratica correlata
Domanda del libro di testo
Solve each inequality. Give the solution set using interval notation. See Example 10. -9 ≤ x + 5 ≤ 15
69
views
Domanda del libro di testo
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 4(2x + 7) = 2x + 22 + 3(2x + 2)
75
views
Domanda del libro di testo
Solve each quadratic equation using the zero-factor property. See Example 5. 4x² - 4x + 1 = 0
68
views
Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. 2x² - x - 28 = 0
57
views
Domanda del libro di testo
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 2(x - 8) = 3x - 16
60
views