Sure, let's solve these equations step-by-step.
### Equation 19: [tex]\(\frac{x + 11}{8} = -3\)[/tex]
1. To isolate [tex]\(x\)[/tex], first multiply both sides by 8:
[tex]\[ x + 11 = -3 \cdot 8 \][/tex]
2. Perform the multiplication on the right-hand side:
[tex]\[ x + 11 = -24 \][/tex]
3. Subtract 11 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = -24 - 11 \][/tex]
[tex]\[ x = -35 \][/tex]
So, the solution for [tex]\(x\)[/tex] in equation 19 is [tex]\(-35\)[/tex].
### Equation 20: [tex]\(\frac{n - 5}{-2} = -7\)[/tex]
1. To isolate [tex]\(n\)[/tex], first multiply both sides by -2:
[tex]\[ n - 5 = -7 \cdot -2 \][/tex]
2. Perform the multiplication on the right-hand side:
[tex]\[ n - 5 = 14 \][/tex]
3. Add 5 to both sides to solve for [tex]\(n\)[/tex]:
[tex]\[ n = 14 + 5 \][/tex]
[tex]\[ n = 19 \][/tex]
So, the solution for [tex]\(n\)[/tex] in equation 20 is [tex]\(19\)[/tex].
### Equation 21: [tex]\(1 = \frac{a - 13}{-6}\)[/tex]
1. To isolate [tex]\(a\)[/tex], first multiply both sides by -6:
[tex]\[ a - 13 = 1 \cdot -6 \][/tex]
2. Perform the multiplication on the right-hand side:
[tex]\[ a - 13 = -6 \][/tex]
3. Add 13 to both sides to solve for [tex]\(a\)[/tex]:
[tex]\[ a = -6 + 13 \][/tex]
[tex]\[ a = 7 \][/tex]
So, the solution for [tex]\(a\)[/tex] in equation 21 is [tex]\(7\)[/tex].
### Equation 22: [tex]\(4 = \frac{w + 8}{9}\)[/tex]
1. To isolate [tex]\(w\)[/tex], first multiply both sides by 9:
[tex]\[ w + 8 = 4 \cdot 9 \][/tex]
2. Perform the multiplication on the right-hand side:
[tex]\[ w + 8 = 36 \][/tex]
3. Subtract 8 from both sides to solve for [tex]\(w\)[/tex]:
[tex]\[ w = 36 - 8 \][/tex]
[tex]\[ w = 28 \][/tex]
So, the solution for [tex]\(w\)[/tex] in equation 22 is [tex]\(28\)[/tex].
To summarize, the solutions are:
- Equation 19: [tex]\(x = -35\)[/tex]
- Equation 20: [tex]\(n = 19\)[/tex]
- Equation 21: [tex]\(a = 7\)[/tex]
- Equation 22: [tex]\(w = 28\)[/tex]
