We can solve the inequality \( 5(x + 8) - 7 < 23 \) step by step:

### Step 1: Expand the expression on the left-hand side.
\[
5(x + 8) = 5x + 40
\]
Now substitute that back into the inequality:
\[
5x + 40 - 7 < 23
\]
Simplify further:
\[
5x + 33 < 23
\]

### Step 2: Subtract 33 from both sides.
\[
5x < 23 - 33
\]
\[
5x < -10
\]

### Step 3: Divide both sides by 5.
\[
x < \frac{-10}{5}
\]
\[
x < -2
\]

Thus, the solution is \( x < -2 \).

Would you like further details on this, or do you have any questions?

Here are 5 related questions:
1. How would the solution change if the inequality was \( \leq \) instead of \( < \)?
2. How do you graph the solution \( x < -2 \) on a number line?
3. What happens if you divide by a negative number in an inequality?
4. How would the inequality change if the constant on the right-hand side was different?
5. How do inequalities change when multiplying both sides by a variable?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

Explore how to solve the inequality 5(x+8)-7<23 using algebraic techniques. This guide includes a breakdown of key steps like expanding expressions and handling inequalities. Perfect for students in Grades 6-8, this solution provides clear explanations for mastering inequalities.

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