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Difficulty:
5%
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Question Stats:
96% (01:28) correct
4%
(01:55)
wrong
based on 209
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If b is one of the solutions of the equation |4x - 3| = |x + 6|, then 3b + 5 = ?
A) 14
B) 18
C) 4
D) 12
E) 6
A) 14
B) 18
C) 4
D) 12
E) 6
1) 4x-3 = x+6 // -(4x-3) = -(x+6)
=> 3x = 9
=> x = 3 = b
So, 3b+5 = 14
OR
2) -(4x-3) = x+6 // 4x-3 = -(x+6)
=> -5x = 3
=> x = -3/2 = b
So, 3b + 5 =1/2
One of these solutions is the answer. Therefore, the right choice is A
=> 3x = 9
=> x = 3 = b
So, 3b+5 = 14
OR
2) -(4x-3) = x+6 // 4x-3 = -(x+6)
=> -5x = 3
=> x = -3/2 = b
So, 3b + 5 =1/2
One of these solutions is the answer. Therefore, the right choice is A
Updated on: 22 Jul 2025, 06:08
Originally posted by BrushMyQuant on 24 Oct 2023, 09:43.
Last edited by BrushMyQuant on 22 Jul 2025, 06:08, edited 1 time in total.
Last edited by BrushMyQuant on 22 Jul 2025, 06:08, edited 1 time in total.
b is one of the solutions of the equation |4x -3| = |x+6| and we need to find the value of 3b+5
|4x - 3| = |x + 6|
Squaring both the sides we get
\((4x-3)^2 = (x+6)^2\)
=> \(16x^2 - 2*4x*3 + 9 = x^2 + 2*x*6 + 36\)
=> \(15x^2 - 24x - 12x -27 = 0\)
=> \(15x^2 - 36x - 27 = 0\)
Dividing all terms by 3 we get
\(5x^2 - 12x - 9 = 0\)
=> \(5x^2 - 15x + 3x - 9 = 0\)
=> 5x*(x - 3) + 3*(x - 3) = 0
=> (x-3) * (5x+3) = 0
=> x = 3 or \(\frac{-3}{5}\)
=> b = 3 or \(\frac{-3}{5}\)
We need to find the value of 3b + 5 and all option choices are integers
=> b = 3
=> 3b + 5 = 3*3 + 5 = 14
So, Answer will be A
Hope it helps!
Absolute Values Theory and Solved Problems Playlist Link here
Watch the following video to MASTER Absolute Values
_________________
|4x - 3| = |x + 6|
Squaring both the sides we get
\((4x-3)^2 = (x+6)^2\)
=> \(16x^2 - 2*4x*3 + 9 = x^2 + 2*x*6 + 36\)
=> \(15x^2 - 24x - 12x -27 = 0\)
=> \(15x^2 - 36x - 27 = 0\)
Dividing all terms by 3 we get
\(5x^2 - 12x - 9 = 0\)
=> \(5x^2 - 15x + 3x - 9 = 0\)
=> 5x*(x - 3) + 3*(x - 3) = 0
=> (x-3) * (5x+3) = 0
=> x = 3 or \(\frac{-3}{5}\)
=> b = 3 or \(\frac{-3}{5}\)
We need to find the value of 3b + 5 and all option choices are integers
=> b = 3
=> 3b + 5 = 3*3 + 5 = 14
So, Answer will be A
Hope it helps!
Absolute Values Theory and Solved Problems Playlist Link here
Watch the following video to MASTER Absolute Values
_________________
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GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
PhlpSrks
Your second solution is wrong I believe and should be x = b = -3/5
-4x + 3 = x +6
-5x = 3
x = -3/5
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