Question

Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of

Answer 1

The possible values of x are 5 and -1/12

Complete question

Given that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x

How to determine the possible values of x?

The ratio is given as:

2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1

Express as fraction

$\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}$

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

Read more about ratios at:

brainly.com/question/2328454

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