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Sagot :
Let's solve each equation step by step.
### Equation 1: [tex]\( 5x + 4 = 49 \)[/tex]
1. Subtract 4 from both sides:
[tex]\[ 5x + 4 - 4 = 49 - 4 \][/tex]
[tex]\[ 5x = 45 \][/tex]
2. Divide both sides by 5:
[tex]\[ \frac{5x}{5} = \frac{45}{5} \][/tex]
[tex]\[ x = 9 \][/tex]
### Equation 2: [tex]\( 3x + 1 = 31 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 3x + 1 - 1 = 31 - 1 \][/tex]
[tex]\[ 3x = 30 \][/tex]
2. Divide both sides by 3:
[tex]\[ \frac{3x}{3} = \frac{30}{3} \][/tex]
[tex]\[ x = 10 \][/tex]
### Equation 3: [tex]\( 7x + 1 = 36 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 7x + 1 - 1 = 36 - 1 \][/tex]
[tex]\[ 7x = 35 \][/tex]
2. Divide both sides by 7:
[tex]\[ \frac{7x}{7} = \frac{35}{7} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 4: [tex]\( 9x + 1 = 91 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 9x + 1 - 1 = 91 - 1 \][/tex]
[tex]\[ 9x = 90 \][/tex]
2. Divide both sides by 9:
[tex]\[ \frac{9x}{9} = \frac{90}{9} \][/tex]
[tex]\[ x = 10 \][/tex]
### Equation 5: [tex]\( 2x + 9 = 13 \)[/tex]
1. Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 = 13 - 9 \][/tex]
[tex]\[ 2x = 4 \][/tex]
2. Divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{4}{2} \][/tex]
[tex]\[ x = 2 \][/tex]
### Equation 6: [tex]\( 8x + 8 = 64 \)[/tex]
1. Subtract 8 from both sides:
[tex]\[ 8x + 8 - 8 = 64 - 8 \][/tex]
[tex]\[ 8x = 56 \][/tex]
2. Divide both sides by 8:
[tex]\[ \frac{8x}{8} = \frac{56}{8} \][/tex]
[tex]\[ x = 7 \][/tex]
### Equation 7: [tex]\( 3x + 9 = 30 \)[/tex]
1. Subtract 9 from both sides:
[tex]\[ 3x + 9 - 9 = 30 - 9 \][/tex]
[tex]\[ 3x = 21 \][/tex]
2. Divide both sides by 3:
[tex]\[ \frac{3x}{3} = \frac{21}{3} \][/tex]
[tex]\[ x = 7 \][/tex]
### Equation 8: [tex]\( 1x + 3 = 8 \)[/tex]
1. Subtract 3 from both sides:
[tex]\[ 1x + 3 - 3 = 8 - 3 \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 9: [tex]\( 4x + 2 = 26 \)[/tex]
1. Subtract 2 from both sides:
[tex]\[ 4x + 2 - 2 = 26 - 2 \][/tex]
[tex]\[ 4x = 24 \][/tex]
2. Divide both sides by 4:
[tex]\[ \frac{4x}{4} = \frac{24}{4} \][/tex]
[tex]\[ x = 6 \][/tex]
### Summary of Solutions:
- For [tex]\( 5x + 4 = 49 \)[/tex], [tex]\( x = 9 \)[/tex]
- For [tex]\( 3x + 1 = 31 \)[/tex], [tex]\( x = 10 \)[/tex]
- For [tex]\( 7x + 1 = 36 \)[/tex], [tex]\( x = 5 \)[/tex]
- For [tex]\( 9x + 1 = 91 \)[/tex], [tex]\( x = 10 \)[/tex]
- For [tex]\( 2x + 9 = 13 \)[/tex], [tex]\( x = 2 \)[/tex]
- For [tex]\( 8x + 8 = 64 \)[/tex], [tex]\( x = 7 \)[/tex]
- For [tex]\( 3x + 9 = 30 \)[/tex], [tex]\( x = 7 \)[/tex]
- For [tex]\( 1x + 3 = 8 \)[/tex], [tex]\( x = 5 \)[/tex]
- For [tex]\( 4x + 2 = 26 \)[/tex], [tex]\( x = 6 \)[/tex]
Thus, the list of solutions is:
[tex]\[ [9.0, 10.0, 5.0, 10.0, 2.0, 7.0, 7.0, 5.0, 6.0] \][/tex]
### Equation 1: [tex]\( 5x + 4 = 49 \)[/tex]
1. Subtract 4 from both sides:
[tex]\[ 5x + 4 - 4 = 49 - 4 \][/tex]
[tex]\[ 5x = 45 \][/tex]
2. Divide both sides by 5:
[tex]\[ \frac{5x}{5} = \frac{45}{5} \][/tex]
[tex]\[ x = 9 \][/tex]
### Equation 2: [tex]\( 3x + 1 = 31 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 3x + 1 - 1 = 31 - 1 \][/tex]
[tex]\[ 3x = 30 \][/tex]
2. Divide both sides by 3:
[tex]\[ \frac{3x}{3} = \frac{30}{3} \][/tex]
[tex]\[ x = 10 \][/tex]
### Equation 3: [tex]\( 7x + 1 = 36 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 7x + 1 - 1 = 36 - 1 \][/tex]
[tex]\[ 7x = 35 \][/tex]
2. Divide both sides by 7:
[tex]\[ \frac{7x}{7} = \frac{35}{7} \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 4: [tex]\( 9x + 1 = 91 \)[/tex]
1. Subtract 1 from both sides:
[tex]\[ 9x + 1 - 1 = 91 - 1 \][/tex]
[tex]\[ 9x = 90 \][/tex]
2. Divide both sides by 9:
[tex]\[ \frac{9x}{9} = \frac{90}{9} \][/tex]
[tex]\[ x = 10 \][/tex]
### Equation 5: [tex]\( 2x + 9 = 13 \)[/tex]
1. Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 = 13 - 9 \][/tex]
[tex]\[ 2x = 4 \][/tex]
2. Divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{4}{2} \][/tex]
[tex]\[ x = 2 \][/tex]
### Equation 6: [tex]\( 8x + 8 = 64 \)[/tex]
1. Subtract 8 from both sides:
[tex]\[ 8x + 8 - 8 = 64 - 8 \][/tex]
[tex]\[ 8x = 56 \][/tex]
2. Divide both sides by 8:
[tex]\[ \frac{8x}{8} = \frac{56}{8} \][/tex]
[tex]\[ x = 7 \][/tex]
### Equation 7: [tex]\( 3x + 9 = 30 \)[/tex]
1. Subtract 9 from both sides:
[tex]\[ 3x + 9 - 9 = 30 - 9 \][/tex]
[tex]\[ 3x = 21 \][/tex]
2. Divide both sides by 3:
[tex]\[ \frac{3x}{3} = \frac{21}{3} \][/tex]
[tex]\[ x = 7 \][/tex]
### Equation 8: [tex]\( 1x + 3 = 8 \)[/tex]
1. Subtract 3 from both sides:
[tex]\[ 1x + 3 - 3 = 8 - 3 \][/tex]
[tex]\[ x = 5 \][/tex]
### Equation 9: [tex]\( 4x + 2 = 26 \)[/tex]
1. Subtract 2 from both sides:
[tex]\[ 4x + 2 - 2 = 26 - 2 \][/tex]
[tex]\[ 4x = 24 \][/tex]
2. Divide both sides by 4:
[tex]\[ \frac{4x}{4} = \frac{24}{4} \][/tex]
[tex]\[ x = 6 \][/tex]
### Summary of Solutions:
- For [tex]\( 5x + 4 = 49 \)[/tex], [tex]\( x = 9 \)[/tex]
- For [tex]\( 3x + 1 = 31 \)[/tex], [tex]\( x = 10 \)[/tex]
- For [tex]\( 7x + 1 = 36 \)[/tex], [tex]\( x = 5 \)[/tex]
- For [tex]\( 9x + 1 = 91 \)[/tex], [tex]\( x = 10 \)[/tex]
- For [tex]\( 2x + 9 = 13 \)[/tex], [tex]\( x = 2 \)[/tex]
- For [tex]\( 8x + 8 = 64 \)[/tex], [tex]\( x = 7 \)[/tex]
- For [tex]\( 3x + 9 = 30 \)[/tex], [tex]\( x = 7 \)[/tex]
- For [tex]\( 1x + 3 = 8 \)[/tex], [tex]\( x = 5 \)[/tex]
- For [tex]\( 4x + 2 = 26 \)[/tex], [tex]\( x = 6 \)[/tex]
Thus, the list of solutions is:
[tex]\[ [9.0, 10.0, 5.0, 10.0, 2.0, 7.0, 7.0, 5.0, 6.0] \][/tex]
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