https://file.aiquickdraw.com/mathbot/file/1725808676322xksgknfd.jpg

The inequality in the image is:

\[
15 - 2x \leq 3
\]

To solve for \(x\), follow these steps:

1. **Isolate the term with \(x\)**:
   \[
   15 - 2x \leq 3
   \]
   Subtract 15 from both sides:
   \[
   -2x \leq 3 - 15
   \]
   Simplify the right side:
   \[
   -2x \leq -12
   \]

2. **Solve for \(x\)**:
   Divide both sides by \(-2\). Remember that dividing or multiplying an inequality by a negative number reverses the inequality sign:
   \[
   x \geq \frac{-12}{-2}
   \]
   Simplify:
   \[
   x \geq 6
   \]

So the solution to the inequality is \( x \geq 6 \).

Would you like further details or have any questions?

Here are some related questions to consider:

1. How does multiplying or dividing by a negative number affect inequalities?
2. What is the importance of reversing the inequality sign in this problem?
3. Can you graph the solution \( x \geq 6 \) on a number line?
4. How would the solution change if the inequality was strict (\(<\) instead of \(\leq\))?
5. What happens if the inequality had been \(15 + 2x \leq 3\)?

**Tip:** Always check the sign of the coefficient when solving inequalities, especially when dealing with negative numbers, as it affects the direction of the inequality.

Learn how to solve the linear inequality 15 - 2x ≤ 3 using simple algebraic steps. This problem involves isolating the variable and applying the rule of reversing the inequality when dividing by a negative number. Ideal for students in Grades 7-9.

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