An algebra problem by Christopher Boo

Algebra Level 2

I've drawn 2 numbers, $x+1$ and $x+2$ , on a number line. Is it true that the distance between $x+1$ and $0$ is greater than the distance between $x+2$ and $0?$

Yes, it is always true No, but it is sometimes true No, it is always false

1 solution

Tapas Mazumdar
Jun 9, 2017

The distance between two points on a number line can be expressed as the modulus of their difference. From the problem, we should have

$|x+1 - 0| > |x+2 - 0| \implies |x+1| > |x+2|$

The above inequality is satisfied only when $x < -\dfrac 32$ . Thus the statement is true but not always true. $\star$

An algebra problem by Christopher Boo

1 solution

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