Question

What numbers are a distance of 3/4 unit from 1/8 on a number line? Select the locations on the number line to plot the points.

Answer 1

3/4 = 6/8. so 6/8-1/8= 5/8. 5/8 is the answer.

Answer 2

`(7)/(8)\text{ and }-(5)/(8)`

Explanation:

Let x be the number which is
`(3)/(4)` unit from
`(1)/(8)`,

That is,

`|x-(1)/(8)| =(3)/(4)`

`x-(1)/(8)=\pm (3)/(4)`

`x=(1)/(8)\pm (3)/(4)`

`\implies x=(1)/(8)+(3)/(4)\text{ or }x=(1)/(8)-(3)/(4)`

`x=(1+6)/(8)\text{ or }x=(1-6)/(8)`

`x=(7)/(8)\text{ or }x=-(5)/(8)`

Hence, 7/8 and -5/8 are 3/4 unit far from 1/8 on the number line.