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
Subtract 2 from both sides to isolate : Thus, the solution to the inequality is .
Step 2: Graphical Representation
To graph the solution, imagine a number line:
- Mark the point on the number line.
- Since the inequality is strict (), use an open circle at to indicate that is not included.
- Shade all the values to the left of , as they satisfy the inequality .
Graph:
On a number line, it would look like this:
---o------------------>
4
Where the open circle at and the arrow indicates that the solution includes all values less than 4.
Would you like further details, or have any questions?
Related Questions:
- What if the inequality were ?
- How would you solve ?
- What changes in the solution if the inequality is ?
- Can you solve ?
- How do you represent graphically?
Tip: When solving inequalities, remember that the inequality direction flips if you multiply or divide by a negative number.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Formulas
Linear inequality manipulation
Theorems
Properties of inequalities
Suitable Grade Level
Grades 6-8