The image shows solutions to the inequality x≤−1

Question

. How many solutions are there between −4
and −5
?

(1 point)
Responses

There are 99 solutions: all the decimals from −4.01
to −4.99
.
There are 99 solutions: all the decimals from negative 4.01 to negative 4.99 .

There are 9,999 solutions: all the decimals from −4.0001
to −4.9999
.
There are 9,999 solutions: all the decimals from negative 4.0001 to negative 4.9999 .

There are 999 solutions: all the decimals from −4.001
to −4.999
.
There are 999 solutions: all the decimals from negative 4.001 to negative 4.999 .

an infinite number

Answer 1

The inequality \( x \leq -1 \) means that \( x \) can take any value less than or equal to \(-1\).

When considering the interval between \(-4\) and \(-5\), which actually refers to all the values between these two points, we can look for potential solutions:

• The range between \(-4\) and \(-5\) includes all the decimal values between those two numbers, such as \(-4.1\), \(-4.01\), \(-4.001\) etc.
• Since there are infinitely many decimal values that can be placed between any two chosen points on the number line, there are not just a finite number of solutions.

Therefore, the correct answer is:

an infinite number.