Let's solve each of the equations step by step.
### i) [tex]\(5x - 3 = 3x + 7\)[/tex]
1. Move the [tex]\(3x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[
5x - 3 - 3x = 7
\][/tex]
2. Simplify the left side:
[tex]\[
2x - 3 = 7
\][/tex]
3. Move the constant term [tex]\(-3\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[
2x = 7 + 3
\][/tex]
4. Simplify the right side:
[tex]\[
2x = 10
\][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{10}{2}
\][/tex]
[tex]\[
x = 5
\][/tex]
So, the solution is [tex]\( x = 5 \)[/tex].
### ii) [tex]\(4x + 2 = 2x - 6\)[/tex]
1. Move the [tex]\(2x\)[/tex] term from the right side to the left side to isolate the variable terms on one side:
[tex]\[
4x + 2 - 2x = -6
\][/tex]
2. Simplify the left side:
[tex]\[
2x + 2 = -6
\][/tex]
3. Move the constant term [tex]\(2\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[
2x = -6 - 2
\][/tex]
4. Simplify the right side:
[tex]\[
2x = -8
\][/tex]
5. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-8}{2}
\][/tex]
[tex]\[
x = -4
\][/tex]
So, the solution is [tex]\( x = -4 \)[/tex].
### iii) [tex]\(4x + 5 = 13\)[/tex]
1. Move the constant term [tex]\(5\)[/tex] from the left side to the right side to isolate the variable term:
[tex]\[
4x + 5 - 5 = 13 - 5
\][/tex]
2. Simplify both sides:
[tex]\[
4x = 8
\][/tex]
3. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8}{4}
\][/tex]
[tex]\[
x = 2
\][/tex]
So, the solution is [tex]\( x = 2 \)[/tex].
### Summary
The solutions for the given equations are:
i) [tex]\( x = 5 \)[/tex]
ii) [tex]\( x = -4 \)[/tex]
iii) [tex]\( x = 2 \)[/tex]
