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.