Absolutely! Let's solve each of these equations step-by-step in detail:
### (i) Equation: [tex]\(2 + y = 7\)[/tex]
1. To isolate [tex]\(y\)[/tex], subtract 2 from both sides of the equation:
[tex]\[
2 + y - 2 = 7 - 2
\][/tex]
2. Simplifying both sides gives:
[tex]\[
y = 5
\][/tex]
So, the solution for [tex]\(y\)[/tex] is [tex]\(5\)[/tex].
### (ii) Equation: [tex]\(2a - 3 = 5\)[/tex]
1. To isolate [tex]\(a\)[/tex], first add 3 to both sides of the equation:
[tex]\[
2a - 3 + 3 = 5 + 3
\][/tex]
2. Simplifying both sides gives:
[tex]\[
2a = 8
\][/tex]
3. To solve for [tex]\(a\)[/tex], divide both sides by 2:
[tex]\[
a = \frac{8}{2}
\][/tex]
4. Simplifying the right side gives:
[tex]\[
a = 4
\][/tex]
So, the solution for [tex]\(a\)[/tex] is [tex]\(4\)[/tex].
### (iii) Equation: [tex]\(10 - q = 6\)[/tex]
1. To isolate [tex]\(q\)[/tex], we first subtract 10 from both sides of the equation:
[tex]\[
10 - q - 10 = 6 - 10
\][/tex]
2. Simplifying both sides gives:
[tex]\[
-q = -4
\][/tex]
3. To solve for [tex]\(q\)[/tex], multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
q = -1 \times (-4)
\][/tex]
4. Simplifying the right side gives:
[tex]\[
q = 4
\][/tex]
So, the solution for [tex]\(q\)[/tex] is [tex]\(4\)[/tex].
### Summary
- [tex]\(y = 5\)[/tex] from equation (i)
- [tex]\(a = 4\)[/tex] from equation (ii)
- [tex]\(q = 4\)[/tex] from equation (iii)
Thus, the solutions are:
[tex]\[
y = 5, \quad a = 4, \quad q = 4
\][/tex]
