Explanation Given Information: The given rational inequality is | x + 2 x − 1 | ≤ 3 . Formula used: Following steps have been followed during the solution of the equation, Step 1. If x is given by | x | that means x has two values one for positive x and another for negative x . Solve the equation for both the cases. Step 2. Change the inequality symbol ≤ to = , and solve the equation. Step 3. Divide the number lines in between the obtained points, consequently intervals will be found. Step 4. Find out the sign of the function in those intervals by plugging in any test value from that interval into the equation. Step 5. Find out those intervals for which the function satisfies the inequality ≤ or ≥ . Calculation: Consider the inequality, | x + 2 x − 1 | ≤ 3 First solve inequality for positive fraction value, x + 2 x − 1 ≤ 3 Now to find the values of x , set the ≤ to = x + 2 x − 1 = 3 Multiplying by ( x − 1 ) in both sides, ( x − 1 ) ⋅ ( x + 2 x − 1 ) = ( x − 1 ) ⋅ 3 x + 2 = 3 x − 3 2 x = 5 x = 5 2 Now solve for negative fraction value, − ( x + 2 ) ( x − 1 ) ≤ 3 Now to find the values of x , set the ≤ to = − x + 2 x − 1 = 3 Multiplying by ( x − 1 ) in both sides, ( x − 1 ) ⋅ ( − x + 2 x − 1 ) = ( x − 1 ) ⋅ 3 − x − 2 = 3 x − 3 4 x = 1 x = 1 4 And, find the value to make the denominator 0 . x − 1 = 0 x = 1 These three points will divide the number line in four intervals as, Now check whether the inequality | x + 2 x − 1 | ≤ 3 is satisfied or not

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ISBN: 9780321877949

Author: Johnson

Publisher: YUZU

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Chapter 11.9, Problem 62ES

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Chapter 11.9, Problem 61ES

Chapter 11.9, Problem 63ES

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Chapter 11 Solutions

EBK ELEMENTARY AND INTERMEDIATE ALGEBRA

Ch. 11.1 - Solve: 64=y2.Ch. 11.1 - Solve: t2=10. Give exact solutions and...Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 5YT Ch. 11.1 - 6. Solve: . Ch. 11.1 - Prob. 7YT Ch. 11.1 - Prob. 8YT Ch. 11.1 - Prob. 9YT Ch. 11.1 - Prob. 10YT

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The solution of the rational inequality | x + 2 x − 1 | ≤ 3 .

Solution Summary: The author explains the formula used to calculate the rational inequality left|x+2

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Chapter 11 Solutions