https://r2.erweima.ai/mathbot/image/1725548763294qkfv5iab.jpg

The inequality in the image is:

\[
x - 7 < 2 - 5x
\]

Let's solve this step by step:

### Step 1: Move all terms involving \(x\) to one side.
Add \(5x\) to both sides of the inequality:

\[
x + 5x - 7 < 2
\]
This simplifies to:
\[
6x - 7 < 2
\]

### Step 2: Isolate \(x\).
Add 7 to both sides to get rid of the \(-7\):

\[
6x < 2 + 7
\]
Simplifying this:

\[
6x < 9
\]

### Step 3: Solve for \(x\).
Divide both sides by 6:

\[
x < \frac{9}{6}
\]
Simplifying:

\[
x < \frac{3}{2}
\]

### Final Answer:
\[
x < 1.5
\]

Would you like further explanation or have any questions?

Here are five related questions to consider:
1. How do you solve inequalities with variables on both sides?
2. What changes when multiplying or dividing inequalities by negative numbers?
3. How would the solution change if the inequality was \(x - 7 \leq 2 - 5x\)?
4. Can you graph the solution \(x < 1.5\) on a number line?
5. How do you check if a solution to an inequality is correct?

**Tip:** Always remember to reverse the inequality symbol when multiplying or dividing by a negative number!

Learn how to solve the linear inequality x - 7 < 2 - 5x with a detailed step-by-step solution. This problem covers key algebraic concepts, including moving variables and isolating terms. Suitable for students in Grades 8-10.

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