https://file.aiquickdraw.com/mathbot/file/1726782839995sxqcu0ln.jpg

The inequality in the image reads:

\[
2 - 7(5x - 2) \leq -19
\]

Let's solve this step-by-step:

### Step 1: Expand the terms
Distribute the \(-7\) across the terms inside the parentheses:

\[
2 - 7(5x) + 7(2) \leq -19
\]

This simplifies to:

\[
2 - 35x + 14 \leq -19
\]

### Step 2: Combine like terms
Add \(2\) and \(14\) on the left-hand side:

\[
16 - 35x \leq -19
\]

### Step 3: Isolate the variable term
Subtract \(16\) from both sides:

\[
-35x \leq -19 - 16
\]

\[
-35x \leq -35
\]

### Step 4: Solve for \(x\)
Divide both sides by \(-35\), and remember to reverse the inequality sign when dividing by a negative number:

\[
x \geq 1
\]

### Solution:
\[
x \geq 1
\]

Let me know if you'd like any further details!

Here are 5 related questions to consider:
1. How would the solution change if the inequality were strict (i.e., \( < \) instead of \( \leq \))?
2. What is the graphical representation of the inequality \( x \geq 1 \) on a number line?
3. Can this inequality be expressed in interval notation?
4. How would the solution differ if there were different coefficients inside the parentheses?
5. How does multiplying or dividing both sides of an inequality by a negative number affect the inequality sign?

**Tip**: Always remember to flip the inequality sign when you multiply or divide by a negative number!

Learn how to solve the linear inequality 2 - 7(5x - 2) <= -19 with detailed step-by-step solutions. This example explores the distributive property and key rules in algebra. Suitable for students in Grades 8-10.

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