a) 3x + 1> 2x OR 3x + 1 < 5x – 2, b) 3x + 1 > 2x AND 3x + 1 < 5x – 2.

Q: Explain why the inequality x2 + x + 1 &gt; 0 has all realnumbers as the solution set.

A: Inequality x2 + x + 1 &gt; 0 has all real numbers as the solution set.

Q: Solve the following inequality graphically in two-dimensional plane: x &gt; – 3

A: We first draw the line x=-3

Q: express the given inequality in interval notation. x &gt; 6

A: The given inequality is x&gt;6.

Q: An inequality that can be written in the form Ax + By&lt; C (where A and B are not both zero) is…

A: By definition,Linear inequalities in two variables are of the form

Q: On her test, Zipporah submitted the follow asked to solve the inequality -2x +5211. Zipporah's Work:

A: Introduction: Equations and inequalities are both mathematical sentences that are formed by…

Q: Find the solution in interval notation to the linear inequality: 8<2- 4x < 14.

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Q: Prove that the Intermediate Value Theorem remains true when the inequality sign is flipped, i.e.…

A: We know that According to Intermediate Value Theorem: A function is continuous in interval  I = [a ,…

Q: The inequality, x ≤ 4, written in interval notation is : 1. (-∞,4) 2. [-∞,4) 3. (-∞,4] 4. [-∞0,4] O…

A: Inequality: A mathematical expression in which both sides are not equal is called an inequality. We…

Q: Solve the following inequalities and show their solution sets on the real line. 2x - 1 &lt; x + 3

A: 2x-1&lt;x+3Substract x from both side2x-1-x&lt;x+3-xx-1&lt;3

Q: If |2| = 2, use the triangle inequality to show that |Im(1 – z+ 22)| <7 and 2 – 4z² + 3| 2 3.

A: the given question is related to complex numbers. the solution is explained below.

Q: STION 16 implify the inequality z² + 2z < 15.

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Q: 8 Given: mZP + mZR < 180. PQ < QR Write an inequality to describe the re- strictions on x. (7x-18)…

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Q: Express the interval using inequalities. (a) (2, 0) (b) [-3, -1] (c) [0, 9)

A: The given interval is 2,∞. The given open interval indicates all the real numbers greater than 2.…

Q: What is the solution (in interval notation) to the following inequality below: 6 < -6 x O [-1,0] O…

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Q: What is the solution (in interval notation) to the following inequality below? 9-2x<7 + 2(x - 3) O…

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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: Find the Domain of the following inequalities and solve them In x +1

A: Given

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

A: The given inequality is,

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: Find the supremum and infimum of the set {x € R|10/T – I > 0}, if they exist. If they exist, provide…

A:

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: express the given inequality in interval notation and sketch a graph of the interval. x &gt; 1

A: Given: Inequality x &gt; 1 To Find: To express the given inequality in interval notation and to…

Q: express the given inequality in interval notation. x ≤ 0

A: We have to express the given inequality in interval notation. x ≤ 0

Q: What is the solution (in interval notation) to the following inequality below: 2 (x+4)-3xs 14

A: Given: - The inequality is, 2(x+4)-3x≤14 To find: -The solution of the given inequality (in interval…

Q: Find the values of x that satisfies the inequality. 3.x+1 <1 2. 3. 2

A: The solution is given below in next steps.

Q: What is the solution (in interval notation) to the following inequality below? 7x+2< 17 - 3x 0 (-)…

A:

Q: Express the inequality in interval notation, and then graph the corresponding interval. 0 ≤ x ≤ 1/2

A: Given:           0≤x≤12 Inequality in interval notation        0,12

Q: Let ƒ(x) = x² + 2 x – 2. Find all the values satisfying f(x) < x² + 2. - NOTE: Enter an inequality…

A: Given f(x)=x2+2x-2

Q: V2sec(x) > 2

A: Given, 2secx ≥ 2                        We have to solve the inequality in the interval  0, 2π

Q: 1. Use the Intermediate Value Theorem to show that there exists at least one solution in the set of…

A:

Q: Determine the largest integer value of x in the solution of the following inequality. 3x – 3 < –16 -…

A:

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: 3x4 - x2 - 4 < 2 x3 + 12 x

A: Given: 3x4-x2-4 &lt; 2x3 +12x

Q: Which one is the inequality shown by the followly детари + эх -1 enci 6) xsi ус у сі д h) X<I узі b)…

A: An inequality can be represented graphically as a region on one side of a line. Inequalities that…

Q: 7) Sketch in the xy-pkane the set of all of numbers (x,4) that salisfy all the following three 4x +…

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Q: Solve the Inequalities and show the solution sets and explain that on the real line. whereas n =39…

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Q: express the given inequality in interval notation and sketch a graph of the interval. x ≤ 0

A: x≤0 It means the set of all real numbers less than or equal to zero.  Therefore given inequality in…

Q: A recent study showed that 75% of all people have a commute time to work of 15 minutes or more. The…

A: There should be pinstead of μin the last statement. Given: Margin of ErrorE=0.08 The percentage of…

Q: Describe in words the region of R(all real numbers)^3 represented by the inequalities 1 < x2 + y 2 +…

A: Note: it is assumed that the inequality is 1&lt;x2+y2+z2-3z≤4 .   The equation of a sphere in 3D…

Q: Find the real number which satisfies the given inequality- X²-2X + 3 ˃ 0

A: Given query is to find solution of the inequality.

Q: Solve the inequalities and show the Solution Sets On the veal line,

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Q: Match each compound inequality on the left to the graph that represents its solution on the ri 3 5n…

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Q: Use the mean value theorem to establish the following inequalities: x-1 b) 1 -

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Q: Solve the inequalities and show the Solution Sets On the veal line.

A: As per guideline we have to solve one question

Q: Show the solution to this inequality with a number line. -(x – 1)(2x + 7)(x+2) < 0

A: Given  -x-12x+7x+2≤0 Multiplying by -1 on both sides, the inequality sign gets reversed.…

Q: How would you convince someone that there are infinitely many ordered pairs of real numbers that…

A: How would you convince someone that there are infinitely many ordered pairs of real numbers that…

Q: express the given inequality in interval notation and sketch a graph of the interval. x ≤ 2

A: The given inequality is x ≤ 2

Q: Suppose that we have found a value of 8 such that ε = What numbers should go in the blanks such that…

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Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

A: