Let's solve the inequality step by step.

The given inequality is:

\[
3x - 7 \geq 2(x - 7)
\]

### Step 1: Expand the right-hand side
Distribute the \(2\) on the right side:

\[
3x - 7 \geq 2x - 14
\]

### Step 2: Move terms involving \(x\) to one side
Subtract \(2x\) from both sides to move the terms with \(x\) to the left:

\[
3x - 2x - 7 \geq -14
\]

Simplify:

\[
x - 7 \geq -14
\]

### Step 3: Move constant terms to the other side
Now, add \(7\) to both sides to isolate \(x\):

\[
x \geq -14 + 7
\]

Simplify:

\[
x \geq -7
\]

### Final Answer:
\[
x \geq -7
\]

This means that \(x\) can be any value greater than or equal to \(-7\).

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Would you like more details or further clarification?

Here are some related questions you can explore:

1. How do you solve linear inequalities with fractions?
2. What happens if we multiply or divide both sides of an inequality by a negative number?
3. Can you solve quadratic inequalities in a similar way?
4. How do you graph the solution of an inequality on a number line?
5. What is the difference between solving an equation and solving an inequality?

**Tip:** Always remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol!

Learn how to solve the linear inequality 3x−7≥2(x−7) step by step. This explanation covers the distributive property, solving linear inequalities, and the basic properties of inequalities. Suitable for students in Grades 7-9.

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