Let's solve the equations step by step.

a) $3x - 8 = 4 - x$

1. Add $x$ to both sides to bring $x$ terms to one side: $3x + x - 8 = 4$ $4x - 8 = 4$

2. Add 8 to both sides to isolate $4x$: $4x = 12$

3. Divide by 4 to solve for $x$: $x = 3$

b) $x - 14 = \frac{x}{2}$

1. Multiply through by 2 to eliminate the fraction: $2(x - 14) = x$

2. Expand the left side: $2x - 28 = x$

3. Subtract $x$ from both sides: $x - 28 = 0$

4. Add 28 to solve for $x$: $x = 28$

Final Solutions:

• $a) \, x = 3$
• $b) \, x = 28$

Do you want further details or have additional questions?

Related Questions:

1. How can you verify the solution to equation (a)?
2. What happens if you move $x$ terms in the opposite direction in equation (a)?
3. How can you rewrite equation (b) in a different form to make it easier to solve?
4. What if equation (b) had a negative coefficient instead of $\frac{x}{2}$?
5. How do these methods generalize to more complex linear equations?

Tip: Always check your solutions by substituting them back into the original equations.