Skip to main content
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 31
Capitolo 2, Problema 31

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. -9x ≥ 36

Guida verificata passo dopo passo
1
Start with the given inequality: \(-9x \geq 36\).
To isolate \(x\), divide both sides of the inequality by \(-9\). Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be reversed.
After dividing, the inequality becomes: \(x \leq \frac{36}{-9}\).
Simplify the fraction on the right side to find the numerical value.
Express the solution in interval notation and then graph the solution set on a number line, showing all values of \(x\) that satisfy the inequality.

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:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Solving Linear Inequalities

A linear inequality involves an inequality symbol (>, <, ≥, ≤) with a linear expression. To solve it, isolate the variable on one side by performing inverse operations, similar to solving linear equations, but be mindful of inequality rules.
Video consigliato:
06:07
Linear Inequalities

Multiplying or Dividing by a Negative Number

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. This is crucial to maintain the truth of the inequality and avoid incorrect solutions.
Video consigliato:
04:22
Dividing Complex Numbers

Interval Notation and Graphing Solution Sets

Interval notation expresses solution sets using parentheses or 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.
Video consigliato:
05:18
Interval Notation
Pratica correlata
Domanda del libro di testo

Simplify and write the result in standard form. √-108

1045
views
Domanda del libro di testo

Solve each radical equation in Exercises 11–30. Check all proposed solutions. 1+4x=1+x\(\sqrt{1 + 4\sqrt{x}\)} = 1 + \(\sqrt{x}\)

757
views
Domanda del libro di testo

Solve each equation in Exercises 15–34 by the square root property. (8x - 3)2 = 5

754
views
Domanda del libro di testo

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

1019
views
1
rank
Domanda del libro di testo

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1

878
views
Domanda del libro di testo

An automobile repair shop charged a customer \$1182, listing \$357 for parts and the remainder for labor. If the cost of labor is \$75 per hour, how many hours of labor did it take to repair the car?

706
views