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Ch. 1 - Equations and Inequalities
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 1 - Equations and InequalitiesProblem 7
Chapter 2, Problem 7

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≤ 7
List of absolute value equations and inequalities matched with number line graphs showing solution sets between -7 and 7.

Verified step by step guidance
1
Understand the inequality \(|x| \leq 7\). The absolute value \(|x|\) represents the distance of \(x\) from 0 on the number line, so this inequality means the distance from 0 is less than or equal to 7.
Rewrite the inequality without the absolute value by considering the definition: \(|x| \leq 7\) is equivalent to \(-7 \leq x \leq 7\).
Interpret the solution set \(-7 \leq x \leq 7\) as all real numbers \(x\) between -7 and 7, including the endpoints -7 and 7.
Look for the graph in Column II that shows a line segment or interval on the number line starting at -7 and ending at 7, with solid dots or closed circles at both ends to indicate inclusion of the endpoints.
Confirm that the graph matches the interval \([-7, 7]\) and that no other graphs represent this solution set.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value Inequality

An absolute value inequality like |x| ≤ 7 represents all values of x whose distance from zero on the number line is less than or equal to 7. This means x lies between -7 and 7, inclusive. Understanding this helps in identifying the solution set as an interval.
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Interval Notation and Graphing

Interval notation expresses the set of solutions compactly, such as [-7, 7] for |x| ≤ 7. Graphing this interval on a number line involves shading all points between -7 and 7, including the endpoints, to visually represent the solution set.
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Interval Notation

Matching Equations to Graphs

Matching equations or inequalities to their graphs requires recognizing the solution set's shape and boundaries. For |x| ≤ 7, the graph is a line segment from -7 to 7. This skill involves interpreting algebraic expressions and linking them to their visual representations.
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Related Practice
Textbook Question

Decide whether each statement is true or false. If false, correct the right side of the equation. √-25 = 5i

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≠ 7

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Textbook Question

Solve each problem. Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the mixture? A. 24% B. 30% C. 31% D. 33%

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Textbook Question

Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.)

A. 5x+3 =11

B.12x+6 =-4

C.100x =50(x+3)

D. 6(x+4) =x+24

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Textbook Question

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

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Textbook Question

Match each equation in Column I with the correct first step for solving it in Column II. √(x+5) = 7

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