Answer :
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]
### 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]
