> Explanation Approach: If a is a real number, the absolute value of a is defined as | a | = { a , when a ≥ 0 − a , when a < 0 . The following table illustrates the solution for the absolute value inequalities of the form | x | < k , | x | ≤ k , | x | > k and | x | ≥ k , where k > 0. Absolute Value Inequalities Solution | x | < k , for k > 0 − k < x < k | x | ≤ k , for k > 0 − k ≤ x ≤ k | x | > k , for k > 0 x < − k or x > k | x | ≥ k , for k > 0 x ≤ − k or x ≥ k Addition and subtraction property of inequality: When a number is added or subtracted on both sides of the inequality, the inequality remains the same. If a < b and k is a constant, then ( a + k ) < ( b + k ) and ( a − k ) < ( b − k )

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 1.8, Problem 81E

To determine

To Express:

The inequality |t−78°|≤8° without using absolute value symbol.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.8, Problem 80E

Chapter 1.8, Problem 82E

Students have asked these similar questions

Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

+ Theorem: Let be a function from a topological space (X,T) on to a non-empty set y then is a quotient map iff vesy if f(B) is closed in X then & is >Y. ie Bclosed in bp closed in the quotient topology induced by f iff (B) is closed in x- التاريخ Acy الموضوع : Theorem:- IP & and I are topological space and fix sy is continuous او function and either open or closed then the topology Cony is the quatient topology p proof: Theorem: Lety have the quotient topology induced by map f of X onto y. The-x: then an arbirary map g:y 7 is continuous 7. iff gof: x > z is "g of continuous Continuous function f

Chapter 1 Solutions

College Algebra (MindTap Course List)

Ch. 1.1 - Self Check 1 Find the restriction on a: 5a+5=3aa2 Ch. 1.1 - Self Check 2 Find the solution set: 4(x3)=7x3 Ch. 1.1 - Self Check 3 Find the solution set: 23p3=p6 Ch. 1.1 - Self Check 4 Solve and classify as an identity, a...Ch. 1.1 - Self Check 5 Solve 35+7x+2=2 Ch. 1.1 - Self Check 6 Solve C=59(F32) for F Ch. 1.1 - Self Check 7 Solve pq=fq+fp for f Ch. 1.1 - Fill in the blanks. If a number satisfies an...Ch. 1.1 - Fill in the blanks. If an equation is true for all...Ch. 1.1 - Prob. 3E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

To Express: The inequality | t − 78 ° | ≤ 8 ° without using absolute value symbol.

Solution Summary: The author illustrates the solution for the Absolute Value Inequalities of the form left|xright|k,

Videos

To Express:

The inequality |t−78°|≤8° without using absolute value symbol.

Want to see the full answer?

Chapter 1 Solutions

To Express: The inequality | t − 78 ° | ≤ 8 ° without using absolute value symbol.

Solution Summary: The author illustrates the solution for the Absolute Value Inequalities of the form left|xright|k,

Videos

To Express: The inequality |t−78°|≤8° without using absolute value symbol.

Want to see the full answer?

Chapter 1 Solutions

To Express:

The inequality |t−78°|≤8° without using absolute value symbol.