Let's solve both equations step-by-step.
### Equation (i): [tex]\(3x - 9 = 4x - 3\)[/tex]
1. Isolate the variable [tex]\(x\)[/tex]:
- Start by getting all the [tex]\(x\)[/tex] terms on one side of the equation and the constant terms on the other side.
- Subtract [tex]\(4x\)[/tex] from both sides to move the [tex]\(x\)[/tex] terms to one side:
[tex]\(3x - 9 - 4x = -3\)[/tex]
2. Simplify the equation:
- Combine like terms: [tex]\(3x - 4x = -x\)[/tex]
- So now, the equation looks like: [tex]\(-x - 9 = -3\)[/tex]
3. Move the constant term to the other side:
- Add 9 to both sides to isolate [tex]\(-x\)[/tex]:
[tex]\(-x - 9 + 9 = -3 + 9\)[/tex]
- Which simplifies to: [tex]\(-x = 6\)[/tex]
4. Solve for [tex]\(x\)[/tex]:
- Multiply both sides by [tex]\(-1\)[/tex] to get the value of [tex]\(x\)[/tex]:
[tex]\(x = -6\)[/tex]
So, the solution for equation (i) is [tex]\(x = -6\)[/tex].
### Equation (ii): [tex]\(3(x - 4) = 21\)[/tex]
1. Expand the equation:
- Distribute the 3 on the left-hand side:
[tex]\(3(x - 4) = 21\)[/tex]
becomes
[tex]\(3x - 12 = 21\)[/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
- Add 12 to both sides to move the constant term:
[tex]\(3x - 12 + 12 = 21 + 12\)[/tex]
- Which simplifies to: [tex]\(3x = 33\)[/tex]
3. Solve for [tex]\(x\)[/tex]:
- Divide both sides by 3:
[tex]\(\frac{3x}{3} = \frac{33}{3}\)[/tex]
- Which gives: [tex]\(x = 11\)[/tex]
So, the solution for equation (ii) is [tex]\(x = 11\)[/tex].
### Summary of Solutions:
- For equation (i) [tex]\(3x - 9 = 4x - 3\)[/tex], the solution is [tex]\(x = -6\)[/tex].
- For equation (ii) [tex]\(3(x - 4) = 21\)[/tex], the solution is [tex]\(x = 11\)[/tex].
