Let's solve the given equations step by step through the trial and error method:
### (i) \(5x - 3 = 12\)
1. Assume an initial value for \( x \) and substitute it into the equation to check if it satisfies the equation:
- Let's try \( x = 2 \):
[tex]\[
5(2) - 3 = 10 - 3 = 7 \quad (\text{Not equal to 12})
\][/tex]
- Let's try \( x = 3 \):
[tex]\[
5(3) - 3 = 15 - 3 = 12 \quad (\text{Equal to 12})
\][/tex]
So, \( x = 3 \) is the solution.
### (ii) \(7y + 3 = -21\)
1. Assume an initial value for \( y \) and substitute it into the equation to check if it satisfies the equation:
- Let's try \( y = -3 \):
[tex]\[
7(-3) + 3 = -21 + 3 = -18 \quad (\text{Not equal to -21})
\][/tex]
- Let's try \( y = -4 \):
[tex]\[
7(-4) + 3 = -28 + 3 = -25 \quad (\text{Not equal to -21})
\][/tex]
- Let's try \( y = -3.5 \):
[tex]\[
7(-3.4285714285714284) + 3 = -24 + 3 = -21 \quad (\text{Equal to -21})
\][/tex]
So, \( y \approx -3.4285714285714284 \) is the solution.
### (iii) \(2y - 5 = 17\)
1. Assume an initial value for \( y \) and substitute it into the equation to check if it satisfies the equation:
- Let's try \( y = 10 \):
[tex]\[
2(10) - 5 = 20 - 5 = 15 \quad (\text{Not equal to 17})
\][/tex]
- Let's try \( y = 11 \):
[tex]\[
2(11) - 5 = 22 - 5 = 17 \quad (\text{Equal to 17})
\][/tex]
So, \( y = 11 \) is the solution.
### (iv) \(4z - 6 = 10\)
1. Assume an initial value for \( z \) and substitute it into the equation to check if it satisfies the equation:
- Let's try \( z = 3 \):
[tex]\[
4(3) - 6 = 12 - 6 = 6 \quad (\text{Not equal to 10})
\][/tex]
- Let's try \( z = 4 \):
[tex]\[
4(4) - 6 = 16 - 6 = 10 \quad (\text{Equal to 10})
\][/tex]
So, \( z = 4 \) is the solution.
In summary, the solutions are:
1. \( x = 3 \)
2. \( y \approx -3.4285714285714284 \)
3. \( y = 11 \)
4. [tex]\( z = 4 \)[/tex]
