To solve the inequality \(2k - 7 < 7k + 6\), we'll isolate \( k \) by following these steps:

### Step 1: Move all terms involving \( k \) to one side.
Subtract \( 2k \) from both sides:

\[
2k - 7 - 2k < 7k + 6 - 2k
\]

This simplifies to:

\[
-7 < 5k + 6
\]

### Step 2: Move the constant term to the other side.
Subtract \( 6 \) from both sides:

\[
-7 - 6 < 5k + 6 - 6
\]

Simplifying further:

\[
-13 < 5k
\]

### Step 3: Isolate \( k \) by dividing by 5.
Divide both sides by \( 5 \):

\[
\frac{-13}{5} < k
\]

Simplifying gives:

\[
k > -\frac{13}{5}
\]

So, the solution is:

\[
k > -\frac{13}{5}
\]

### Final Answer:
\[
k > -\frac{13}{5} \text{ or } k > -2.6
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you solve inequalities with variables on both sides?
2. What are the rules for dividing inequalities by a negative number?
3. How can we represent the solution of this inequality on a number line?
4. How does this inequality change if we reverse the direction of the inequality sign?
5. What are some real-life applications of solving inequalities?

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

Learn how to solve the linear inequality 2k−7<7k+6 with a detailed step-by-step explanation. This problem focuses on essential algebraic concepts such as isolating variables and the properties of inequalities. Perfect for students in Grades 7-10.

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