Does the Transitive Property of Inequality hold true for four real numbers a, b, c, and d? That is, is the following statement true? If a < b, b < c, and c < d, then a < d.

Q: 2x? +x 2 3 nswer:

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Q: The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is…

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Q: Solve the following compound inequality. Write the solution in set-builder notation. 6-2x>14 and…

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Q: What is the fundamental inequality of arithmetic and geometric means of n numbers X. X3.. X, " Under…

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Q: Show that if |a − 5| &lt; 1/2 and |b − 8| &lt; 1/2, then|(a + b) − 13| &lt; 1. Hint: Use the…

A: We have, a-5&lt;12; b-8&lt;12.We have to show that a+b - 13 &lt; 1Consider a+b - 13 = a + b -13…

Q: For the given inequality 5 < <8 1. Verbally describe the subset of real number that the inequality…

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Q: It is never possible to solve an inequality that has a number on each side. O True O False

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Q: (1) that the reverse triangle inequality holds for all real numbers. (HINT: Write a as a - b+ b.…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: Solve the following absolute value inequality. Provide your answer as: a) double inequality, b) in…

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Q: of the inequality x + y > 1 because when 3 is substituted for ,the true statement The ordered pair…

A: Consider the inequality x+y&gt;1 -(i)Substituting for x=3 and y=2 in the inequality given by…

Q: Identify each value of z that makes the below inequality true. – (3x +1) > -7+3x - -1 20 1 0. -32

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Q: In n is a natural number, for which real numbers is the inequality (1+ æ)" >1+ nx true? A x -1 x 1…

A: Let's find.

Q: Solve the following inequality algebraically. x2 + 3x – 28 > 0 Answer: Submit Answer or (,] (,) All…

A: The given inequality is x2+3x-28&gt;0

Q: Solve the following inequality and graph the solution set on a number line. 5(x + 1) - 9< 4x +1

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Q: In n is a natural number, for which real numbers is the inequality (1 + æ)" > 1+ nx true?

A: 1+xn≥1+nx When n=1, we get ⇒1+x1≥1+1·x⇒1+x≥1+x Which is true. Therefore given statement is true for…

Q: Consider the following inequality:−2x−4&gt;−18Step 1 of 2 : Write the solution using interval…

A: The given inequality is,

Q: 5. If k is a positive real number, then the inequality |x| < k is equivalent to < x <

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Q: Find all the real numbers x which satisfy the inequality 1 7— 2х (2л — 7)2 and carefully sketch the…

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Q: Use the triangle inequality to establish the following inequalities: (b) ||c| – |d|| \p - 기 ()…

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Q: The set of all solutions of the inequality 2|2x + 2] > 12 is

A: Given inequality  22x+2≥12 the above equation can be written as  2(2x+2)≥12 and 2(2x+2)≤-12…

Q: (a) The set of all points on the real line whose distance from zero is less than 9 can be described…

A: here given that all points on real line whose distance from 0 to us less than 3

Q: From the given inequality, what is the value of x in the converted form of the inequality? If your…

A: given, 2x+ 8y &gt;79 --------------------------(i) &amp; 2x-5y &gt;-38…

Q: How many solutions are there to the inequality I1 +12 +r3 < 11 where r1, r2, and r3 are nonnegative…

A: The inequality is x1+x2+x3≤11. Case i: x1+x2+x3=11 The value of n is 11. Then,…

Q: Indicate for which natural numbers n the given inequality is true. Prove your answers by induction.…

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Q: Solve the following inequality algebraically. x2 – 16x + 60 > 0 Answer: Submit Answer or [ ) (, ] (,…

A: solve the following inequality

Q: Determine the smallest integer value of x in the solution of the following inequality.−2x+10≤1

A: *to find:- the smallest value of x.

Q: The reflexive property of equality states that if a=b then b=a.

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Q: Fill in the blank with an appropriate inequality symbol.(a) If x  5, then x  3 2.(b) If x  5,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: State all integer values of x in the interval -4, 2 that satisfy the following inequality: 4x + 5 <…

A: Given,          4x+5&lt;-6  , -4,2

Q: State all integer values of x in the interval -4, 2 that satisfy the following inequality: 4x + 5 <…

A: Given the inequality  4x + 5 &lt; -6 We need to find the values of x which satisfies the given…

Q: 1. Fill in the blank with an appropriate inequality symbol. (a) If x 2, then -3x -6. (d) If x < -2,…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Solve the following inequality algebraically. x2 – 18x + 80 > 0 Answer: Submit Answer )61 ) or All…

A: Factories the polynomial and check the sign of multiplication

Q: 4. For the inequality 3"+1 >n determine the set of natural numbers for which it holds.

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Q: 6. If k is a positive real number, then the inequality |x|> k is equivalent to x < or x k.

A: A detailed solution is given below.

Q: Prove the inequality x² + x² + ... + x² n IV 2 2+...+ ²₂ ) ² n

A: Explanation of the answer is as follows

Q: For the inequality 3n+1 > n determine the set of natural numbers for which it holds.

A: (4) For n=1, 32=9&gt;14=1 Assume for n=k then 3k+1&gt;k4.

Q: Which of the following values are solutions to the inequality 4 > x +4? I. - 2 П. - 7 III. 0 O None…

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Q: State all integer values of x in the interval -2 3

A: To solve the given inequality: 5x+5≥ 3

Q: 3x4 - x2 - 4 < 2 x3 + 12 x

A: Given: 3x4-x2-4 &lt; 2x3 +12x

Q: raph the solution set of the following linear Inequality. -7y + 7x 2 -7y + 42

A: -7y+7x≥-7y+42 7y-7y+7x≥7y-7y+42                7x≥42                  x≥6 Type of boundary line…

Q: An inequality which is satisfied by all the permissible values of x is an absolute inequality, which…

A: Since we know that square of any positive/negative/zero number is greater and equal to zero .…

Q: The negative multiplication property of inequality states that if a < b and c is negative, then ac

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Q: For the inequality 3"+1 > n4 determine the set of natural numbers for which it holds.

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Q: Which of the following statements is false about inequalities? O If we add a negative number to both…

A: option 1 Add a negative number say -3 to both sides of the inequality 3&lt;5 -3+3&lt;5-3 0&lt;2 True…

Q: Solve the following inequality algebraically.

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Q: If a is a nonnegative real number, then which inequality statement best describes a?(a) a &lt; 0 (b)…

A: A non negative real number includes all positive real numbers and zero. Hence, if a is a…

Q: Determine the smallest integer value of x in the solution of the following inequality. 3x – 10 > -4

A: The given inequality is 3x-10&gt;-4

Q: Prove the inequality b−ab≤lnba≤b−aa provided 0&lt;a≤b.

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Q: Consider the inequality ax² + bx + c > 0, where a, b, and c are real numbers with a 0. Suppose the…

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