The possible values of x are 5 and -1/12
Given that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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