Let's solve the equations one by one from the image:

(a) $4x + 1 = 2x + 7$

1. Subtract $2x$ from both sides: $4x - 2x + 1 = 7$ $2x + 1 = 7$
2. Subtract 1 from both sides: $2x = 6$
3. Divide by 2: $x = 3$

(b) $5x + 4 = 3x + 16$

1. Subtract $3x$ from both sides: $5x - 3x + 4 = 16$ $2x + 4 = 16$
2. Subtract 4 from both sides: $2x = 12$
3. Divide by 2: $x = 6$

(c) $2x + 8 = x + 12$

1. Subtract $x$ from both sides: $2x - x + 8 = 12$ $x + 8 = 12$
2. Subtract 8 from both sides: $x = 4$

(d) $7x + 1 = 2x + 46$

1. Subtract $2x$ from both sides: $7x - 2x + 1 = 46$ $5x + 1 = 46$
2. Subtract 1 from both sides: $5x = 45$
3. Divide by 5: $x = 9$

Solutions:

• (a) $x = 3$
• (b) $x = 6$
• (c) $x = 4$
• (d) $x = 9$

Would you like further explanation on any of these steps or more details on solving linear equations?

Here are five questions for further practice:

1. What is the solution to $6x + 2 = 3x + 14$?
2. Solve $4x + 9 = 5x + 5$.
3. What is $x$ if $8x - 3 = 5x + 10$?
4. Solve $9x + 6 = 7x + 16$.
5. What happens if you multiply both sides of $2x + 1 = 3x - 5$ by 2 before solving?

Tip: When solving linear equations, always move the variables to one side and constants to the other to simplify the equation.