Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary

Let's solve the inequality:

\[
6h - 5(h - 1) \leq 7h - 11
\]

### Step 1: Expand the terms on the left side
Distribute the \(-5\) through \((h - 1)\):

\[
6h - 5(h - 1) = 6h - 5h + 5 = h + 5
\]

So, the inequality becomes:

\[
h + 5 \leq 7h - 11
\]

### Step 2: Isolate the variable
Subtract \(h\) from both sides:

\[
5 \leq 6h - 11
\]

### Step 3: Add 11 to both sides to simplify:

\[
5 + 11 \leq 6h
\]

\[
16 \leq 6h
\]

### Step 4: Solve for \(h\)
Divide both sides by 6:

\[
\frac{16}{6} \leq h
\]

Simplify \(\frac{16}{6}\) to \(\frac{8}{3}\):

\[
\frac{8}{3} \leq h
\]

### Final Solution:
The solution is \(h \geq \frac{8}{3}\).

### Step 5: Write the solution in interval notation
In interval notation, this is:

\[
\left[ \frac{8}{3}, \infty \right)
\]

This means that \(h\) is greater than or equal to \(\frac{8}{3}\).

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Would you like more details or have any questions? 

Here are 5 related questions for you:
1. What are some common methods to solve inequalities?
2. How would the solution change if the inequality were strict (e.g., \(<\) instead of \(\leq\))?
3. How do we represent an inequality on a number line?
4. Can inequalities have no solution or infinite solutions?
5. What are the key differences between solving equations and inequalities?

**Tip**: Always check if you need to reverse the inequality sign when dividing or multiplying by a negative number!

Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary.

Learn how to solve the linear inequality 6h - 5(h - 1) ≤ 7h - 11 with a detailed step-by-step solution. This problem covers key algebraic concepts like the distributive property, isolating variables, and solving inequalities. The solution includes interval notation, ideal for Grades 7-10.

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