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Sagot :
Alright, let's solve each of the given equations step-by-step and verify that the solutions are correct.
1. [tex]\( x + 12 = 20 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 12 from both sides:
[tex]\[ x = 20 - 12 \][/tex]
[tex]\[ x = 8 \][/tex]
- Check: Substitute [tex]\( x = 8 \)[/tex] back into the original equation:
[tex]\[ 8 + 12 = 20 \][/tex]
Since this is true, the solution [tex]\( x = 8 \)[/tex] is correct.
2. [tex]\( x + 44 = 69 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 44 from both sides:
[tex]\[ x = 69 - 44 \][/tex]
[tex]\[ x = 25 \][/tex]
- Check: Substitute [tex]\( x = 25 \)[/tex] back into the original equation:
[tex]\[ 25 + 44 = 69 \][/tex]
Since this is true, the solution [tex]\( x = 25 \)[/tex] is correct.
3. [tex]\( 9 + 6 = x \)[/tex]
- Calculate the sum:
[tex]\[ x = 9 + 6 \][/tex]
[tex]\[ x = 15 \][/tex]
- Check: Substitute [tex]\( x = 15 \)[/tex] back into the original equation:
[tex]\[ 9 + 6 = 15 \][/tex]
Since this is true, the solution [tex]\( x = 15 \)[/tex] is correct.
4. [tex]\( x + 14 = 54 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 14 from both sides:
[tex]\[ x = 54 - 14 \][/tex]
[tex]\[ x = 40 \][/tex]
- Check: Substitute [tex]\( x = 40 \)[/tex] back into the original equation:
[tex]\[ 40 + 14 = 54 \][/tex]
Since this is true, the solution [tex]\( x = 40 \)[/tex] is correct.
5. [tex]\( 45 - 6 = x \)[/tex]
- Calculate the difference:
[tex]\[ x = 45 - 6 \][/tex]
[tex]\[ x = 39 \][/tex]
- Check: Substitute [tex]\( x = 39 \)[/tex] back into the original equation:
[tex]\[ 45 - 6 = 39 \][/tex]
Since this is true, the solution [tex]\( x = 39 \)[/tex] is correct.
6. [tex]\( x + 32 = 47 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 32 from both sides:
[tex]\[ x = 47 - 32 \][/tex]
[tex]\[ x = 15 \][/tex]
- Check: Substitute [tex]\( x = 15 \)[/tex] back into the original equation:
[tex]\[ 15 + 32 = 47 \][/tex]
Since this is true, the solution [tex]\( x = 15 \)[/tex] is correct.
7. [tex]\( x - 39 = 64 \)[/tex]
- Isolate [tex]\( x \)[/tex] by adding 39 to both sides:
[tex]\[ x = 64 + 39 \][/tex]
[tex]\[ x = 103 \][/tex]
- Check: Substitute [tex]\( x = 103 \)[/tex] back into the original equation:
[tex]\[ 103 - 39 = 64 \][/tex]
Since this is true, the solution [tex]\( x = 103 \)[/tex] is correct.
To summarize, the solutions to the equations are:
1. [tex]\( x = 8 \)[/tex]
2. [tex]\( x = 25 \)[/tex]
3. [tex]\( x = 15 \)[/tex]
4. [tex]\( x = 40 \)[/tex]
5. [tex]\( x = 39 \)[/tex]
6. [tex]\( x = 15 \)[/tex]
7. [tex]\( x = 103 \)[/tex]
All solutions have been checked and confirmed to be correct.
1. [tex]\( x + 12 = 20 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 12 from both sides:
[tex]\[ x = 20 - 12 \][/tex]
[tex]\[ x = 8 \][/tex]
- Check: Substitute [tex]\( x = 8 \)[/tex] back into the original equation:
[tex]\[ 8 + 12 = 20 \][/tex]
Since this is true, the solution [tex]\( x = 8 \)[/tex] is correct.
2. [tex]\( x + 44 = 69 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 44 from both sides:
[tex]\[ x = 69 - 44 \][/tex]
[tex]\[ x = 25 \][/tex]
- Check: Substitute [tex]\( x = 25 \)[/tex] back into the original equation:
[tex]\[ 25 + 44 = 69 \][/tex]
Since this is true, the solution [tex]\( x = 25 \)[/tex] is correct.
3. [tex]\( 9 + 6 = x \)[/tex]
- Calculate the sum:
[tex]\[ x = 9 + 6 \][/tex]
[tex]\[ x = 15 \][/tex]
- Check: Substitute [tex]\( x = 15 \)[/tex] back into the original equation:
[tex]\[ 9 + 6 = 15 \][/tex]
Since this is true, the solution [tex]\( x = 15 \)[/tex] is correct.
4. [tex]\( x + 14 = 54 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 14 from both sides:
[tex]\[ x = 54 - 14 \][/tex]
[tex]\[ x = 40 \][/tex]
- Check: Substitute [tex]\( x = 40 \)[/tex] back into the original equation:
[tex]\[ 40 + 14 = 54 \][/tex]
Since this is true, the solution [tex]\( x = 40 \)[/tex] is correct.
5. [tex]\( 45 - 6 = x \)[/tex]
- Calculate the difference:
[tex]\[ x = 45 - 6 \][/tex]
[tex]\[ x = 39 \][/tex]
- Check: Substitute [tex]\( x = 39 \)[/tex] back into the original equation:
[tex]\[ 45 - 6 = 39 \][/tex]
Since this is true, the solution [tex]\( x = 39 \)[/tex] is correct.
6. [tex]\( x + 32 = 47 \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 32 from both sides:
[tex]\[ x = 47 - 32 \][/tex]
[tex]\[ x = 15 \][/tex]
- Check: Substitute [tex]\( x = 15 \)[/tex] back into the original equation:
[tex]\[ 15 + 32 = 47 \][/tex]
Since this is true, the solution [tex]\( x = 15 \)[/tex] is correct.
7. [tex]\( x - 39 = 64 \)[/tex]
- Isolate [tex]\( x \)[/tex] by adding 39 to both sides:
[tex]\[ x = 64 + 39 \][/tex]
[tex]\[ x = 103 \][/tex]
- Check: Substitute [tex]\( x = 103 \)[/tex] back into the original equation:
[tex]\[ 103 - 39 = 64 \][/tex]
Since this is true, the solution [tex]\( x = 103 \)[/tex] is correct.
To summarize, the solutions to the equations are:
1. [tex]\( x = 8 \)[/tex]
2. [tex]\( x = 25 \)[/tex]
3. [tex]\( x = 15 \)[/tex]
4. [tex]\( x = 40 \)[/tex]
5. [tex]\( x = 39 \)[/tex]
6. [tex]\( x = 15 \)[/tex]
7. [tex]\( x = 103 \)[/tex]
All solutions have been checked and confirmed to be correct.
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