Let's solve each of the given equations step-by-step:
1. [tex]\( x - 5 = 7 \)[/tex]
To isolate [tex]\( x \)[/tex], add 5 to both sides of the equation:
[tex]\[ x - 5 + 5 = 7 + 5 \][/tex]
[tex]\[ x = 12 \][/tex]
2. [tex]\( x - 6 = 8 \)[/tex]
To isolate [tex]\( x \)[/tex], add 6 to both sides of the equation:
[tex]\[ x - 6 + 6 = 8 + 6 \][/tex]
[tex]\[ x = 14 \][/tex]
3. [tex]\( x - 7 = 12 \)[/tex]
To isolate [tex]\( x \)[/tex], add 7 to both sides of the equation:
[tex]\[ x - 7 + 7 = 12 + 7 \][/tex]
[tex]\[ x = 19 \][/tex]
4. [tex]\( y - 8 = 15 \)[/tex]
To isolate [tex]\( y \)[/tex], add 8 to both sides of the equation:
[tex]\[ y - 8 + 8 = 15 + 8 \][/tex]
[tex]\[ y = 23 \][/tex]
5. [tex]\( y - 4 = 18 \)[/tex]
To isolate [tex]\( y \)[/tex], add 4 to both sides of the equation:
[tex]\[ y - 4 + 4 = 18 + 4 \][/tex]
[tex]\[ y = 22 \][/tex]
6. [tex]\( y - 3 = 20 \)[/tex]
To isolate [tex]\( y \)[/tex], add 3 to both sides of the equation:
[tex]\[ y - 3 + 3 = 20 + 3 \][/tex]
[tex]\[ y = 23 \][/tex]
7. [tex]\( z - 12 = 21 \)[/tex]
To isolate [tex]\( z \)[/tex], add 12 to both sides of the equation:
[tex]\[ z - 12 + 12 = 21 + 12 \][/tex]
[tex]\[ z = 33 \][/tex]
8. [tex]\( z - 15 = 37 \)[/tex]
To isolate [tex]\( z \)[/tex], add 15 to both sides of the equation:
[tex]\[ z - 15 + 15 = 37 + 15 \][/tex]
[tex]\[ z = 52 \][/tex]
9. [tex]\( z - 18 = -42 \)[/tex]
To isolate [tex]\( z \)[/tex], add 18 to both sides of the equation:
[tex]\[ z - 18 + 18 = -42 + 18 \][/tex]
[tex]\[ z = -24 \][/tex]
10. [tex]\( z - 20 = -30 \)[/tex]
To isolate [tex]\( z \)[/tex], add 20 to both sides of the equation:
[tex]\[ z - 20 + 20 = -30 + 20 \][/tex]
[tex]\[ z = -10 \][/tex]
After solving each equation, we find the following values:
1. [tex]\( x = 12 \)[/tex]
2. [tex]\( x = 14 \)[/tex]
3. [tex]\( x = 19 \)[/tex]
4. [tex]\( y = 23 \)[/tex]
5. [tex]\( y = 22 \)[/tex]
6. [tex]\( y = 23 \)[/tex]
7. [tex]\( z = 33 \)[/tex]
8. [tex]\( z = 52 \)[/tex]
9. [tex]\( z = -24 \)[/tex]
10. [tex]\( z = -10 \)[/tex]
These are the solutions to the given equations.
