Domanda del libro di testo
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x2 - 10x
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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 37
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. 2x - 11 < - 3(x + 2)
Guida verificata passo dopo passo1
Start by distributing the -3 on the right side of the inequality: \(2x - 11 < -3(x + 2)\) becomes \(2x - 11 < -3x - 6\).
Next, add \$3x$ to both sides to get all the $x$ terms on one side: \(2x + 3x - 11 < -3x + 3x - 6\) which simplifies to \(5x - 11 < -6\).
Then, add 11 to both sides to isolate the term with \(x\): \(5x - 11 + 11 < -6 + 11\) which simplifies to \(5x < 5\).
Now, divide both sides by 5 to solve for \(x\): \(\frac{5x}{5} < \frac{5}{5}\) which simplifies to \(x < 1\).
Express the solution in interval notation as \((-\infty, 1)\) and graph this on a number line by shading all values less than 1 with an open circle at 1.
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Solving Linear Inequalities
A linear inequality involves an inequality symbol (<, >, ≤, ≥) with a linear expression. To solve it, isolate the variable by performing algebraic operations similar to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.
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06:07
Linear Inequalities
Interval Notation
Interval notation is a way to represent solution sets of inequalities using parentheses and brackets. Parentheses indicate that an endpoint is not included, while brackets mean it is included. For example, (a, b) means all numbers between a and b, excluding a and b.
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05:18Interval Notation
Graphing Solution Sets on a Number Line
Graphing solution sets involves marking the range of values that satisfy the inequality on a number line. Use open circles for values not included and closed circles for included endpoints. Shade the region representing all solutions to visually communicate the solution set.
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02:35Graphing Lines in Slope-Intercept Form
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