Question

Pls help me with this

Answer 1

x = 1.5

Explanation:

Given

`(x)/(2) \geq 0.75`

`(x)/(2) < 2.5`

Required

Find the value of x.

First, the inequalities need to be rewritten and merged;

if
`(x)/(2) \geq 0.75`, then

`0.75 \leq (x)/(2)`

Multiply both sides by 2

`2 * 0.75 \leq (x)/(2) * 2`

`1.5 \leq x`

Similarly;

`(x)/(2) < 2.5`

Multiply both sides by 2

`2 * (x)/(2) < 2.5 * 2`

`x < 5`

Merging these results together; to give

`1.5 \leq x < 5`

This means that the range of values of x is from 1.5 to 4.9999....

From the question, x is the smallest rational number; from the range above (
`1.5 \leq x < 5`), the minimum value of x is 1.5 and 1.5 is a rational number;

Hence, x = 1.5