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answer:
Given: 3(4x-1)² - 1 = 11
Step-by-Step Solution:
* Add 1 to both sides:
* 3(4x-1)² = 12
* Divide both sides by 3:
* (4x-1)² = 4
* Take the square root of both sides:
* 4x - 1 = ±2
Solving for x:
Case 1: 4x - 1 = 2
* 4x = 3
* x = 3/4
Case 2: 4x - 1 = -2
* 4x = -1
* x = -1/4
Therefore, the solutions for x are:
x = 3/4 or x = -1/4
Answer:
[tex] - \text{For} \: (4x - 1 = 2):[/tex]
[tex]4x - 1 + 1 = 2 + 1[/tex]
[tex]4x = 3[/tex]
[tex]x = \frac{3}{4}[/tex]
[tex] - \text{For} \: {(4x - 1 = -2):}[/tex]
[tex]4x - 1 + 1 = -2 + 1[/tex]
[tex]4x = -1[/tex]
[tex]x = -\frac{1}{4}[/tex]
[tex]x = \frac{3}{4} \quad \text{or} \quad x = -\frac{1}{4}[/tex]