Sure, let's solve the given equations step by step by adding the specified values to both sides and simplifying the result.
(i) Add 6 to both sides of the equation [tex]\( x - 6 = 2 \)[/tex]:
1. Start with the equation:
[tex]\[
x - 6 = 2
\][/tex]
2. Add 6 to both sides:
[tex]\[
x - 6 + 6 = 2 + 6
\][/tex]
3. Simplify both sides:
[tex]\[
x = 8
\][/tex]
So, the resulting equation is:
[tex]\[
x = 8
\][/tex]
(ii) Add 8 to both sides of the equation [tex]\( x - 8 = 0 \)[/tex]:
1. Start with the equation:
[tex]\[
x - 8 = 0
\][/tex]
2. Add 8 to both sides:
[tex]\[
x - 8 + 8 = 0 + 8
\][/tex]
3. Simplify both sides:
[tex]\[
x = 8
\][/tex]
So, the resulting equation is:
[tex]\[
x = 8
\][/tex]
(iii) Add 5 to both sides of the equation [tex]\( 3x + 1 = x - 5 \)[/tex]:
1. Start with the equation:
[tex]\[
3x + 1 = x - 5
\][/tex]
2. Add 5 to both sides:
[tex]\[
3x + 1 + 5 = x - 5 + 5
\][/tex]
3. Simplify both sides:
[tex]\[
3x + 6 = x
\][/tex]
So, the resulting equation is:
[tex]\[
3x + 6 = x
\][/tex]
(iv) Add 9 to both sides of the equation [tex]\( 3x - 9 = 1 - 2x \)[/tex]:
1. Start with the equation:
[tex]\[
3x - 9 = 1 - 2x
\][/tex]
2. Add 9 to both sides:
[tex]\[
3x - 9 + 9 = 1 - 2x + 9
\][/tex]
3. Simplify both sides:
[tex]\[
3x = 10 - 2x
\][/tex]
So, the resulting equation is:
[tex]\[
3x = 10 - 2x
\][/tex]
In summary, the equations after adding the specified values and simplifying are:
- (i) [tex]\( x = 8 \)[/tex]
- (ii) [tex]\( x = 8 \)[/tex]
- (iii) [tex]\( 3x + 6 = x \)[/tex]
- (iv) [tex]\( 3x = 10 - 2x \)[/tex]
