2 - Number Line

Algebra Level 3

In line below the distance between two consecutive points is always the same. What is the value of this distance?

2 3 \frac{2}{3} 3 4 \frac{3}{4} 1 4 \frac{1}{4} 1 2 5 \frac{2}{5}

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

Asîf Múktàdîr
Jun 22, 2015

Let, the distance be y.

Here, 2 × y = x 2 \times y = x

& 3 × y = x 2 3 \times y = x^{2}

So, 4 × y 2 = 3 × y 4 \times y^{2} = 3 \times y

or, 4 × y 2 − 3 × y = 0 4 \times y^{2} - 3 \times y = 0

or, y × ( 4 × y − 3 ) = 0 y\times ( 4 \times y - 3 ) = 0

or, ( 4 × y − 3 ) = 0 ( 4 \times y - 3 ) = 0 { Dividing both sides by y, as the distance, y is not equal to 0 }

or, 4 × y = 3 4 \times y = 3

or, y = 3 4 y = \frac{3}{4}

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