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Find the product of all possible real values of x satisfying
|x + 5|x - 7|| + |6x + 7| x - 7|| = 79
- a)1
- b)163/19
- c)121/13
- d)1334/5
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the product of all possible real values of x satisfying|x + 5|x -...
∣x+5∣x−7∣∣ + ∣6x+7∣x−7∣∣ = 79
Case 1: x > = 7,
∣x+5∣x−7∣∣ + ∣6x+7∣x−7∣∣ = 79
∣x + 5x − 35∣ + ∣6x+7x−49∣ = 79
∣6x−35∣ + ∣13x−49∣ = 79
6x − 35 + 13x − 49 = 79
19x = 163
x = 163/19
Case 2: x < 7,
∣x+5 ∣x−7∣∣ + ∣6x+7∣ x−7∣∣ = 79
∣x−5x + 35 ∣ + ∣6x − 7x + 49∣ = 79
∣35−4x∣ + ∣49−x∣ = 79
35 − 4x + 49 − x = 79
5 × x = 5
x = 1
Product = 163/19
Most Upvoted Answer
Find the product of all possible real values of x satisfying|x + 5|x -...
Solution:
We can observe that x = 7 is not a valid solution since it makes the expression undefined.
| x 5 |x - 7| | 6x 7 | x - 7 | = 79
Let's consider each absolute value separately and we will combine them later.
Case 1: x < />
|x 5| = -(x - 5)
So, the expression becomes:
-(x - 5) * |x - 7| * |6x + 7| * |x - 7| = 79
Case 1.1: x < 5="" and="" 6x="" +="" 7="" />< />
|6x + 7| = -(6x + 7)
-(x - 5) * |x - 7| * -(6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = -79
Case 1.2: x < 5="" and="" 6x="" +="" 7="" /> 0
|6x + 7| = 6x + 7
-(x - 5) * |x - 7| * (6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79
Case 2: x > 5
|x 5| = (x - 5)
So, the expression becomes:
(x - 5) * |x - 7| * |6x + 7| * |x - 7| = 79
Case 2.1: x > 5 and 6x + 7 < />
|6x + 7| = -(6x + 7)
(x - 5) * |x - 7| * -(6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = -79
Case 2.2: x > 5 and 6x + 7 > 0
|6x + 7| = 6x + 7
(x - 5) * |x - 7| * (6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79
Now, we can combine the results from all the cases:
(6x + 7) * (x - 5) * (x - 7)^2 = ±79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79 or (6x + 7) * (x - 5) * (x - 7)^2 = -79
Solving for x, we get:
x = -7/6, 5, 13/3, 7 + 2√
We can observe that x = 7 is not a valid solution since it makes the expression undefined.
| x 5 |x - 7| | 6x 7 | x - 7 | = 79
Let's consider each absolute value separately and we will combine them later.
Case 1: x < />
|x 5| = -(x - 5)
So, the expression becomes:
-(x - 5) * |x - 7| * |6x + 7| * |x - 7| = 79
Case 1.1: x < 5="" and="" 6x="" +="" 7="" />< />
|6x + 7| = -(6x + 7)
-(x - 5) * |x - 7| * -(6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = -79
Case 1.2: x < 5="" and="" 6x="" +="" 7="" /> 0
|6x + 7| = 6x + 7
-(x - 5) * |x - 7| * (6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79
Case 2: x > 5
|x 5| = (x - 5)
So, the expression becomes:
(x - 5) * |x - 7| * |6x + 7| * |x - 7| = 79
Case 2.1: x > 5 and 6x + 7 < />
|6x + 7| = -(6x + 7)
(x - 5) * |x - 7| * -(6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = -79
Case 2.2: x > 5 and 6x + 7 > 0
|6x + 7| = 6x + 7
(x - 5) * |x - 7| * (6x + 7) * |x - 7| = 79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79
Now, we can combine the results from all the cases:
(6x + 7) * (x - 5) * (x - 7)^2 = ±79
Simplifying further:
(6x + 7) * (x - 5) * (x - 7)^2 = 79 or (6x + 7) * (x - 5) * (x - 7)^2 = -79
Solving for x, we get:
x = -7/6, 5, 13/3, 7 + 2√
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Find the product of all possible real values of x satisfying|x + 5|x - 7|| +|6x + 7| x - 7|| = 79a)1b)163/19c)121/13d)1334/5Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the product of all possible real values of x satisfying|x + 5|x - 7|| +|6x + 7| x - 7|| = 79a)1b)163/19c)121/13d)1334/5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the product of all possible real values of x satisfying|x + 5|x - 7|| +|6x + 7| x - 7|| = 79a)1b)163/19c)121/13d)1334/5Correct answer is option 'B'. Can you explain this answer?.
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