Math Problem Statement

Represent the following inequalities on separate number lines. a 1<x<6 b 4<x<11 e 2<x<5 f -8 < x<-1 c -2 <* <6 g 7<88 d -8 <x<3 h 0<x<1

Solution

Let's represent each inequality on separate number lines:

a) 1<x<61 < x < 6

Number line for 1 < x < 6:
0----1----2----3----4----5----6----7
        (-------------------)

b) 4<x<114 < x < 11

Number line for 4 < x < 11:
0----2----4----6----8----10---12
        (-------------------------)

e) 2<x<52 < x < 5

Number line for 2 < x < 5:
0----1----2----3----4----5----6
        (-------------)

f) 8<x<1-8 < x < -1

Number line for -8 < x < -1:
-10----(-8)----(-6)----(-4)----(-2)----0
         (---------------------)

g) 7<x<887 < x < 88

Number line for 7 < x < 88:
0----10----20----30----40----50----60----70----80----90
         (-----------------------------------------------)

d) 8<x<3-8 < x < 3

Number line for -8 < x < 3:
-10----(-8)----(-6)----(-4)----(-2)----0----2----4
         (-----------------------------)

h) 0<x<10 < x < 1

Number line for 0 < x < 1:
0----1
  (---)

For the inequality c) -2 <* <6, it seems to have a typo and is not clear what it's representing. If you meant 2<x<6-2 < x < 6, it would be:

Number line for -2 < x < 6:
-4----(-2)----0----2----4----6----8
         (---------------------)

If you meant something else, please clarify.

Do you want any details or have any questions about these number lines?

Here are some related questions you might ask:

  1. How do you represent x4x \leq 4 on a number line?
  2. Can you explain how to solve a compound inequality?
  3. What does an inequality involving absolute values look like on a number line?
  4. How do you graph x3x \geq -3 on a number line?
  5. How do you combine inequalities to find the solution set?

Tip: When representing inequalities on a number line, use open circles to denote that endpoints are not included and closed circles for endpoints that are included.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Lines

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9