Let's solve the inequality \( 5x + 1 < -x + 7 \) step by step.

1. Start by isolating \( x \) terms on one side of the inequality.
\[
5x + 1 < -x + 7
\]
Add \( x \) to both sides:
\[
6x + 1 < 7
\]

2. Now, subtract 1 from both sides:
\[
6x < 6
\]

3. Finally, divide both sides by 6:
\[
x < 1
\]

Thus, the solution in interval notation is:
\[
(-\infty, 1)
\]

Do you want more details or have any questions?

Here are 5 related questions to expand this:
1. How do you solve inequalities with more complex expressions?
2. What happens if the inequality sign is reversed?
3. How would you solve \( 5x + 1 \leq -x + 7 \) instead?
4. Can you graph the solution on a number line?
5. What happens if you divide both sides of an inequality by a negative number?

**Tip:** When dividing both sides of an inequality by a negative number, remember to reverse the inequality sign.

Learn how to solve the linear inequality 5x + 1 < −x + 7 and express the solution in interval notation. This step-by-step guide covers key algebra concepts like combining like terms and isolating the variable, suitable for students in Grades 7-9.

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