Explanation Given: The inequality is 4 x 2 ≤ 11 x + 3 . Formula used: Zero product property: If a ⋅ b = 0 , then a = 0 , or b = 0 , or a and b both equals to zero. Calculation: Consider the provided inequality. 4 x 2 ≤ 11 x + 3 4 x 2 − 11 x − 3 ≤ 0 Replace the inequality sign with the equal sign and solve for x . 4 x 2 − 11 x − 3 = 0 4 x 2 − 12 x + x − 3 = 0 4 x ( x − 3 ) + 1 ( x − 3 ) = 0 ( x − 3 ) ( 4 x + 1 ) = 0 That is, x = 3 and x = − 1 4 So, the boundary points are − 1 4 and 3. These boundary points separate the number line into three regions. First region: x < − 1 4 Second region: − 1 4 < x < 3 Third region: x > 3 Now, evaluate the quadratic expression 4 x 2 − 11 x − 3 at a test point in each region. For the first region x < − 1 4 , consider a test point x = − 10

Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)

8th Edition

ISBN: 9780134578507

Author: John Tobey Jr., Jeffrey Slater, Jenny Crawford, Jamie Blair

Publisher: PEARSON

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Chapter 8.6, Problem 11E

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To calculate: The solution set for the inequality, 4x2≤11x+3.

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Chapter 8.6, Problem 10E

Chapter 8.6, Problem 12E

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The solution set for the inequality, 4 x 2 ≤ 11 x + 3 .

Solution Summary: The author calculates the solution set for the inequality 4x2le 11x+3.

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To calculate: The solution set for the inequality, 4x2≤11x+3.

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Chapter 8 Solutions