Let's solve both equations from the image step by step:

a) $4x - 3 = 2x + 7$

1. First, subtract $2x$ from both sides to get the variables on one side: $4x - 2x - 3 = 7$ $2x - 3 = 7$

2. Now, add 3 to both sides to isolate the term with $x$: $2x - 3 + 3 = 7 + 3$ $2x = 10$

3. Finally, divide both sides by 2: $x = \frac{10}{2} = 5$

Solution for a) $x = 5$

b) $2x + 6 = 7x - 14$

1. Subtract $2x$ from both sides to get the variables on one side: $6 = 7x - 2x - 14$ $6 = 5x - 14$

2. Add 14 to both sides to move the constant terms to one side: $6 + 14 = 5x - 14 + 14$ $20 = 5x$

3. Finally, divide both sides by 5: $x = \frac{20}{5} = 4$

Solution for b) $x = 4$

Final Answers:

• a) $x = 5$
• b) $x = 4$

Would you like more details or have any questions?

Here are some related questions for you to explore:

1. How would you solve an equation with variables on both sides that include fractions?
2. What happens if you solve an equation and get a false statement, like $5 = 7$?
3. How can you verify your solutions to linear equations by substituting them back into the original equations?
4. How does the process change when you are solving inequalities instead of equations?
5. What are the steps for solving a system of linear equations with two variables?

Tip: When solving linear equations, always aim to isolate the variable by performing inverse operations.