Question

The set of all real numbers x that satisfies 5 5x58 is given by the following interval notation:

[5,8]

Answer 1

The question is a True or False question

Answer:

True

Explanation:

Given

5 ≤ x ≤ 8

Required

Is [5,8] the interval of the given range?

The interval given shows that the range of x begins at 5 and ends 8.

Start by splitting the interval to different inequalities.

1. 5 ≤ x

This implies that 5 is less than or EQUAL TO x;

The keyword needed here is EQUAL TO;

The fact that the inequality gives room for EQUALITY (=) means that the interval begins exactly at 5

2. x ≤ 8

This implies that x is less than or EQUAL TO 8;

Similarly, the keyword needed here is EQUAL TO;

The fact that this inequality gives room for EQUALITY (=) means that the interval ends exactly at 8

So, this implies that the range of values of 5 ≤ x ≤ 8 is 5, 6, 7, 8

And can be represented with [5,8]

So, the statement is true.