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−5≤x≤5

negative 5 less-than-or-equal-to x less-than-or-equal-to 5

−2≤x≤1
negative 2 less-than-or-equal-to x less-than-or-equal-to 1

−5≤x≤−2
negative 5 less-than-or-equal-to x less-than-or-equal-to negative 2

1≤x≤4

1 answer

You have provided several inequalities that define various ranges for the variable \( x \). Here's a summary of each range:

  1. For \( -5 \leq x \leq 5 \):

    • This means \( x \) can take any value from \(-5\) to \(5\), inclusive.

  2. For \( -2 \leq x \leq 1 \):

    • \( x \) can take any value from \(-2\) to \(1\), inclusive.

  3. For \( -5 \leq x \leq -2 \):

    • Here, \( x \) can take values from \(-5\) to \(-2\), inclusive.

  4. For \( 1 \leq x \leq 4 \):

    • In this range, \( x \) can take values from \(1\) to \(4\), inclusive.

If we were to graph these inequalities on a number line, it would be as follows:

  • The first interval \( \left[-5, 5\right] \) includes all values between \(-5\) and \(5\).
  • The second interval \( \left[-2, 1\right] \) overlays part of the first interval, specifically from \(-2\) to \(1\).
  • The third interval \( \left[-5, -2\right] \) is wholly contained within the first interval, specifically from \(-5\) to \(-2\).
  • The fourth interval \( \left[1, 4\right] \) also overlays part of the first interval, starting from \(1\) to \(4\).

If you have any specific questions or need to combine these intervals or perform operations on them, feel free to ask!