Math Problem Statement

A: Show the inequalities on the number line. x>2 -5 -4 -3 -2 -1 0 1 2 3 4 5

Solution

To represent the inequality x>2x > 2 on a number line, you need to indicate all the numbers greater than 2. Here's how you can do it:

  1. Draw a number line with the given range from 5-5 to 55.
  2. Mark the point 22 on the number line.
  3. Since x>2x > 2 does not include the number 22 itself (strict inequality), use an open circle at 22 to indicate that 22 is not part of the solution.
  4. Shade the portion of the number line to the right of 22 to show all numbers greater than 22.

The number line will look like this:

\text{Number Line:} \\ \underline{-5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad \circ 2 \quad \longrightarrow 3 \quad 4 \quad 5} \end{array}$$ The open circle at $$2$$ and the arrow pointing to the right indicate all the numbers greater than $$2$$. Would you like more details or have any questions? Here are 5 related questions to further explore this concept: 1. How would you represent $$x \geq 2$$ on a number line? 2. What does the inequality $$x < -3$$ look like on a number line? 3. How can you represent a compound inequality like $$-1 \leq x < 4$$ on a number line? 4. What does an inequality with no solutions look like on a number line? 5. How would you represent $$x \neq 0$$ on a number line? **Tip:** When using an open circle on a number line, it indicates that the number at that point is not included in the set of solutions. A closed (filled) circle indicates that the number is included.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Line Representation

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9