Sure, I'll provide the step-by-step solution for each equation.
### 1. Solving [tex]\(x + 20 = 70\)[/tex]
To solve for [tex]\(x\)[/tex]:
- Subtract 20 from both sides of the equation.
[tex]\[ x + 20 - 20 = 70 - 20 \][/tex]
[tex]\[ x = 50 \][/tex]
### 2. Solving [tex]\(8x = 24\)[/tex]
To solve for [tex]\(x\)[/tex]:
- Divide both sides of the equation by 8.
[tex]\[ \frac{8x}{8} = \frac{24}{8} \][/tex]
[tex]\[ x = 3.0 \][/tex]
### 3. Solving [tex]\(n - 4 = 100\)[/tex]
To solve for [tex]\(n\)[/tex]:
- Add 4 to both sides of the equation.
[tex]\[ n - 4 + 4 = 100 + 4 \][/tex]
[tex]\[ n = 104 \][/tex]
### 4. Solving [tex]\(7 - x = 10\)[/tex]
To solve for [tex]\(x\)[/tex]:
- Subtract 7 from both sides of the equation to isolate the negative [tex]\(x\)[/tex].
[tex]\[ 7 - x - 7 = 10 - 7 \][/tex]
[tex]\[ -x = 3 \][/tex]
- Multiply both sides by -1 to get [tex]\(x\)[/tex].
[tex]\[ x = -3 \][/tex]
### 5. Solving [tex]\(\frac{y}{8} = 10\)[/tex]
To solve for [tex]\(y\)[/tex]:
- Multiply both sides by 8.
[tex]\[ y = 10 \times 8 \][/tex]
[tex]\[ y = 80 \][/tex]
### 6. Solving [tex]\(\frac{x}{5} + 4 = 15\)[/tex]
To solve for [tex]\(x\)[/tex]:
- Subtract 4 from both sides of the equation.
[tex]\[ \frac{x}{5} + 4 - 4 = 15 - 4 \][/tex]
[tex]\[ \frac{x}{5} = 11 \][/tex]
- Multiply both sides by 5.
[tex]\[ x = 11 \times 5 \][/tex]
[tex]\[ x = 55 \][/tex]
### Summary
- For equation [tex]\(x + 20 = 70\)[/tex], [tex]\(x = 50\)[/tex]
- For equation [tex]\(8x = 24\)[/tex], [tex]\(x = 3.0\)[/tex]
- For equation [tex]\(n - 4 = 100\)[/tex], [tex]\(n = 104\)[/tex]
- For equation [tex]\(7 - x = 10\)[/tex], [tex]\(x = -3\)[/tex]
- For equation [tex]\(\frac{y}{8} = 10\)[/tex], [tex]\(y = 80\)[/tex]
- For equation [tex]\(\frac{x}{5} + 4 = 15\)[/tex], [tex]\(x = 55\)[/tex]
The solutions are:
[tex]\[ \boxed{50, 3.0, 104, -3, 80, 55} \][/tex]
