https://file.aiquickdraw.com/mathbot/file/1727404796904g17teb1q.jpg

The problem in the image contains a system of inequalities to solve and graph:

1. \( 7x + 4 < 4x + 10 \)
2. \( 2 + 6x \leq 11x + 7 \)

Let's solve each inequality step-by-step.

### Inequality 1: \( 7x + 4 < 4x + 10 \)

1. Subtract \( 4x \) from both sides:
   \[
   7x - 4x + 4 < 10
   \]
   \[
   3x + 4 < 10
   \]

2. Subtract 4 from both sides:
   \[
   3x < 6
   \]

3. Divide by 3:
   \[
   x < 2
   \]

### Inequality 2: \( 2 + 6x \leq 11x + 7 \)

1. Subtract \( 6x \) from both sides:
   \[
   2 \leq 5x + 7
   \]

2. Subtract 7 from both sides:
   \[
   -5 \leq 5x
   \]

3. Divide by 5:
   \[
   -1 \leq x
   \]

### Combined Solution:
The solution to the system of inequalities is:
\[
-1 \leq x < 2
\]

### Graphing:
On the number line:
- A **closed circle** at \( x = -1 \) because \( x \geq -1 \) (it includes -1).
- An **open circle** at \( x = 2 \) because \( x < 2 \) (it does not include 2).
- A line connecting the points from \( x = -1 \) to \( x = 2 \).

Would you like me to provide more details or answer any specific questions?

Here are 5 related questions to explore:
1. How would the solution change if the inequality was \( 7x + 4 \leq 4x + 10 \)?
2. What happens when dividing by a negative number in an inequality?
3. How do you graph inequalities involving both greater than and less than?
4. Can you solve a system of inequalities graphically using a coordinate plane?
5. What is the difference between strict inequalities and non-strict inequalities?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Solve and graph: 7x + 4 < 4x + 10 AND 2 + 6x ≤ 11x + 7

Learn how to solve and graph the system of linear inequalities: 7x + 4 < 4x + 10 and 2 + 6x ≤ 11x + 7. This solution covers simplifying inequalities, solving for x, and graphing the solution on a number line. Suitable for students in Grades 7-9.

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