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

Q: What is the triangle inequality? How is it proved? Why is the inequality |a+b| |a|+|b|, where a and…

A: What is the triangle inequality? How is it proved? Why is the inequality |a+b| |a|+|b|, where a and…

Q: Solve the following inequality algebraically. x +14x +40 <0

A: Here the given inequality is  x2+14x+40≤0...(1)

Q: Determine whether each statement is true or false. If the statement is false, make the necessary…

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Q: Solve x - 2 x - 2 and 2x – 1 <x + 2.)

A: Given: x-2&lt; 2x-1&lt; x+2

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: + Prove that if a is a nonzero real number, then 1. 25z? 1 (Hint: Start with the inequality (a - 20,…

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Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: Show All work66($

A: The given inequality is:-7"&gt;∣2x+1∣&gt;−7Separate the inequality into two possible cases. The…

Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: -1 Which compound inequality is graphed? A) x2 B) XS-1 or x>2 x2-1 or x < 2 and 2 2.

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Q: Does the Transitive Property of Inequality hold true for four real numbers a, b, c, and d? That is,…

A: Given: a,b,c,d b are four real numbers. Here, a&lt;b, b&lt;c &amp; c&lt;d

Q: Solve the following inequality. Use the interval not x + a. (- 00, 7] b. (- 00, -7 ] [-7, +00) d.…

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