Solve the inequality and graph the solution on the line provided.
minus, 82, plus, 2, x, is less than, minus, 68
−82+2x<
−68
Answer

Let's solve the inequality step by step.

### The inequality:
\[
-82 + 2x < -68
\]

### Step 1: Add 82 to both sides to isolate the term with \(x\).
\[
2x < -68 + 82
\]
\[
2x < 14
\]

### Step 2: Divide both sides by 2 to solve for \(x\).
\[
x < \frac{14}{2}
\]
\[
x < 7
\]

### Final Solution:
The solution to the inequality is:
\[
x < 7
\]

### Graph the solution on a number line:
To represent this graphically:
- Draw a number line.
- Mark the point \(7\).
- Use an open circle at \(7\) (since \(x\) is **less than** 7, not equal to 7).
- Shade the line to the left of \(7\), indicating that \(x\) is less than \(7\).

Would you like to see the graph, or do you have any questions?

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Here are 5 related questions:
1. How do we graph inequalities with a greater-than sign?
2. What happens when the inequality has a negative coefficient for \(x\)?
3. How would we solve \( -82 + 2x \leq -68 \)?
4. What is the difference between open and closed circles in inequality graphs?
5. Can we have inequalities involving fractions? How are they solved?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

Solve the inequality and graph the solution on the line provided. −82 + 2x < −68

Learn how to solve the inequality −82 + 2x < −68 step-by-step and graph the solution on a number line. This problem covers key algebra concepts, including isolating variables and graphing inequalities. Suitable for students in Grades 6-8.

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