Math Problem Statement

solve the following inequalities and represent the solutions graphically 1.) 2 + x < 6

Solution

Let's solve the inequality:

Step 1: Solve the inequality

2+x<62 + x < 6 Subtract 2 from both sides to isolate xx: x<62x < 6 - 2 x<4x < 4 Thus, the solution to the inequality is x<4x < 4.

Step 2: Graphical Representation

To graph the solution, imagine a number line:

  • Mark the point 44 on the number line.
  • Since the inequality is strict (<<), use an open circle at 44 to indicate that x=4x = 4 is not included.
  • Shade all the values to the left of 44, as they satisfy the inequality x<4x < 4.

Graph:

On a number line, it would look like this:

---o------------------>
   4

Where the open circle at 44 and the arrow indicates that the solution includes all values less than 4.

Would you like further details, or have any questions?

Related Questions:

  1. What if the inequality were 2+x62 + x \leq 6?
  2. How would you solve x3>2x - 3 > 2?
  3. What changes in the solution if the inequality is 2+x>62 + x > 6?
  4. Can you solve 2x+372x + 3 \leq 7?
  5. How do you represent x2x \geq -2 graphically?

Tip: When solving inequalities, remember that the inequality direction flips if you multiply or divide by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Linear inequality manipulation

Theorems

Properties of inequalities

Suitable Grade Level

Grades 6-8