Certainly! Let's go through each equation step-by-step to find the value of [tex]\( x \)[/tex].
### Equation 1: [tex]\( x - 11 = 20 + 5 \)[/tex]
1. Simplify the right-hand side:
[tex]\[
20 + 5 = 25
\][/tex]
2. Rewrite the equation:
[tex]\[
x - 11 = 25
\][/tex]
3. Add 11 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 25 + 11
\][/tex]
4. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 36
\][/tex]
### Equation 2: [tex]\( 11x + 6 = 8 \)[/tex]
1. Subtract 6 from both sides:
[tex]\[
11x = 8 - 6
\][/tex]
2. Simplify the right-hand side:
[tex]\[
8 - 6 = 2
\][/tex]
3. Rewrite the equation:
[tex]\[
11x = 2
\][/tex]
4. Divide both sides by 11:
[tex]\[
x = \frac{2}{11}
\][/tex]
5. Simplify the value of [tex]\( x \)[/tex]:
[tex]\[
x \approx 0.18181818181818182
\][/tex]
### Equation 3: [tex]\( x - 31 = 9 \)[/tex]
1. Add 31 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 9 + 31
\][/tex]
2. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 40
\][/tex]
### Equation 4: [tex]\( x \cdot 5 = 14 + 5 \)[/tex]
1. Simplify the right-hand side:
[tex]\[
14 + 5 = 19
\][/tex]
2. Rewrite the equation:
[tex]\[
5x = 19
\][/tex]
3. Divide both sides by 5:
[tex]\[
x = \frac{19}{5}
\][/tex]
4. Simplify the value of [tex]\( x \)[/tex]:
[tex]\[
x = 3.8
\][/tex]
### Equation 5: [tex]\( x - 3 = 3 + 9 \)[/tex]
1. Simplify the right-hand side:
[tex]\[
3 + 9 = 12
\][/tex]
2. Rewrite the equation:
[tex]\[
x - 3 = 12
\][/tex]
3. Add 3 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 12 + 3
\][/tex]
4. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 15
\][/tex]
### Equation 6: [tex]\( 5 + x = 9 \)[/tex]
1. Subtract 5 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 9 - 5
\][/tex]
2. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
### Equation 7: [tex]\( x + 19 = 33 + 25 \)[/tex]
1. Simplify the right-hand side:
[tex]\[
33 + 25 = 58
\][/tex]
2. Rewrite the equation:
[tex]\[
x + 19 = 58
\][/tex]
3. Subtract 19 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 58 - 19
\][/tex]
4. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 39
\][/tex]
### Summary
The solutions to each equation are:
1. [tex]\( x = 36 \)[/tex]
2. [tex]\( x = \frac{2}{11} \approx 0.18181818181818182 \)[/tex]
3. [tex]\( x = 40 \)[/tex]
4. [tex]\( x = 3.8 \)[/tex]
5. [tex]\( x = 15 \)[/tex]
6. [tex]\( x = 4 \)[/tex]
7. [tex]\( x = 39 \)[/tex]
