Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Lesson Check - Page 204: 4


$x\leq6$ $(-\infty,6]$

Work Step by Step

This number line represents the inequality $x\leq6$. We know that the inequality is not a compound inequality because there is only one endpoint. We know the endpoint, 6, is included in the solution set because of the solid circle used to mark the endpoint. We know the variable is less than or equal to the endpoint because the arrow points to the left, in the direction of decreasing numbers on the number line. The left pointing arrow on the number line means that the left element of the interval notation will be "$-\infty$". The $\infty$ symbol indicates there is no endpoint. The parenthesis indicates that $\infty$ is not a member of the solution set. The right element of the interval notation is "6]", indicating that 6 is included in the solution set, as indicated by the solid circle at the endpoint on the number line.
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