Express the solution set for the compound inequality using interval notation.
-7<4x+1<7

To solve the compound inequality \(-7 < 4x + 1 < 7\), we need to break it into two parts and solve for \(x\).

### Step 1: Solve the left part
\[
-7 < 4x + 1
\]
Subtract 1 from both sides:
\[
-7 - 1 < 4x
\]
\[
-8 < 4x
\]
Divide both sides by 4:
\[
\frac{-8}{4} < x
\]
\[
-2 < x
\]

### Step 2: Solve the right part
\[
4x + 1 < 7
\]
Subtract 1 from both sides:
\[
4x < 7 - 1
\]
\[
4x < 6
\]
Divide both sides by 4:
\[
x < \frac{6}{4}
\]
\[
x < 1.5
\]

### Step 3: Combine the results
We now have the solution:
\[
-2 < x < 1.5
\]
In interval notation, the solution set is:
\[
(-2, 1.5)
\]

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. How do you solve inequalities involving absolute values?
2. What is the difference between "and" and "or" compound inequalities?
3. How do you graph the solution of a compound inequality on a number line?
4. Can compound inequalities have no solution? How would you know?
5. What happens if you multiply or divide an inequality by a negative number?

**Tip:** Always flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Express the solution set for the compound inequality using interval notation. -7 < 4x + 1 < 7

Learn how to solve the compound inequality -7 < 4x + 1 < 7 and express the solution set using interval notation. This problem covers key algebraic concepts related to inequalities and is suitable for students in Grades 7-9.

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