Alright, let's solve these equations step-by-step.
### Part a:
Given equation:
[tex]\[ \frac{3x + 4}{2} = 9.5 \][/tex]
1. Eliminate the fraction by multiplying both sides by 2:
[tex]\[ 3x + 4 = 9.5 \times 2 \][/tex]
2. Calculate the right-hand side:
[tex]\[ 3x + 4 = 19 \][/tex]
3. Isolate \( x \) by subtracting 4 from both sides:
[tex]\[ 3x = 19 - 4 \][/tex]
4. Simplify the equation:
[tex]\[ 3x = 15 \][/tex]
5. Solve for \( x \) by dividing both sides by 3:
[tex]\[ x = \frac{15}{3} \][/tex]
6. Final solution:
[tex]\[ x = 5 \][/tex]
### Part b:
Given equation:
[tex]\[ \frac{7 + 2x}{3} = 5 \][/tex]
1. Eliminate the fraction by multiplying both sides by 3:
[tex]\[ 7 + 2x = 5 \times 3 \][/tex]
2. Calculate the right-hand side:
[tex]\[ 7 + 2x = 15 \][/tex]
3. Isolate \( x \) by subtracting 7 from both sides:
[tex]\[ 2x = 15 - 7 \][/tex]
4. Simplify the equation:
[tex]\[ 2x = 8 \][/tex]
5. Solve for \( x \) by dividing both sides by 2:
[tex]\[ x = \frac{8}{2} \][/tex]
6. Final solution:
[tex]\[ x = 4 \][/tex]
### Summary of Solutions:
- For part a: \( x = 5 \)
- For part b: [tex]\( x = 4 \)[/tex]
