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The inequality given is:

\[
1 - 2x \leq -13
\]

Let's solve it step-by-step:

### Step 1: Isolate the term with \( x \)
Subtract 1 from both sides:

\[
-2x \leq -14
\]

### Step 2: Divide by \(-2\)
To isolate \( x \), divide both sides by \(-2\). Remember, dividing by a negative number reverses the inequality sign.

\[
x \geq 7
\]

### Solution
The solution to the inequality is:

\[
x \geq 7
\]

This means any value of \( x \) that is 7 or greater satisfies the inequality.

Would you like further details, or do you have any questions?

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Here are 5 related questions for further exploration:

1. How would the solution change if the inequality were \( 1 - 2x < -13 \)?
2. What happens to an inequality when multiplying or dividing by a negative number?
3. Can you graph the solution \( x \geq 7 \) on a number line?
4. What if the inequality was \( 1 + 2x \leq -13 \)? How would the solution differ?
5. How can you check if your solution to an inequality is correct?

**Tip:** Always remember to reverse the inequality symbol when you multiply or divide both sides by a negative number!

Learn how to solve the inequality 1 - 2x <= -13 with a step-by-step approach. This solution covers algebraic operations with inequalities and explains how dividing by a negative number affects the inequality sign. Suitable for students in Grades 8-10.

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