Domanda del libro di testo
Find all values of x satisfying the given conditions. y = 2x2 - 3x and y = 2
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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 111
Solve and graph the solution set on a number line: (2x−3)/4 ≥ 3x/4 + 1/2
Guida verificata passo dopo passo1
Start by writing down the inequality: .
To eliminate the denominators, multiply every term on both sides of the inequality by 4, the least common denominator, to simplify the expression.
After multiplying, simplify both sides by distributing and combining like terms where possible.
Isolate the variable on one side by subtracting or adding terms accordingly, and then solve for by dividing or multiplying as needed.
Once you have the inequality in the form or , graph the solution on a number line by shading the region that satisfies the inequality and using a closed or open circle depending on whether the inequality includes equality.
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Solving Linear Inequalities
Solving linear inequalities involves isolating the variable on one side to find the range of values that satisfy the inequality. Similar to equations, operations like addition, subtraction, multiplication, and division are used, but multiplying or dividing by a negative number reverses the inequality sign.
Video consigliato:
06:07
Linear Inequalities
Combining Like Terms and Simplifying Expressions
Combining like terms means adding or subtracting terms with the same variable and exponent to simplify expressions. Simplifying helps to reduce the inequality to a more manageable form, making it easier to isolate the variable and solve.
Video consigliato:
05:07Simplifying Algebraic Expressions
Graphing Solution Sets on a Number Line
Graphing solution sets involves representing all values that satisfy the inequality on a number line. Use a solid dot for inclusive inequalities (≥ or ≤) and an open dot for strict inequalities (> or <), shading the region that represents all possible solutions.
Video consigliato:
02:35Graphing Lines in Slope-Intercept Form
Pratica correlata
Domanda del libro di testo
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x2 - 2x + 2
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Domanda del libro di testo
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x2 - 4x - 5
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Domanda del libro di testo
When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.
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Domanda del libro di testo
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = - (x + 1)2 + 4
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Domanda del libro di testo
In Exercises 107–110, use graphs to find each set. [1,3) ∩ (0,4)
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