Question

What's the Letters number
5(a-2)=2+3a
-8(-5r+7)=7(7r+1)
x-29=-3(3+x)

Answer 1

Let's solve each equation step by step to find the values of \( a \), \( r \), and \( x \).

### Equation 1: \( 5(a-2) = 2 + 3a \)

1. Distribute the 5:
\[
5a - 10 = 2 + 3a
\]

2. Subtract \( 3a \) from both sides:
\[
5a - 3a - 10 = 2
\]
\[
2a - 10 = 2
\]

3. Add 10 to both sides:
\[
2a = 12
\]

4. Divide by 2:
\[
a = 6
\]

### Equation 2: \( -8(-5r + 7) = 7(7r + 1) \)

1. Distribute the -8:
\[
40r - 56 = 49r + 7
\]

2. Subtract \( 40r \) from both sides:
\[
-56 = 9r + 7
\]

3. Subtract 7 from both sides:
\[
-56 - 7 = 9r
\]
\[
-63 = 9r
\]

4. Divide by 9:
\[
r = -7
\]

### Equation 3: \( x - 29 = -3(3 + x) \)

1. Distribute the -3:
\[
x - 29 = -9 - 3x
\]

2. Add \( 3x \) to both sides:
\[
x + 3x - 29 = -9
\]
\[
4x - 29 = -9
\]

3. Add 29 to both sides:
\[
4x = 20
\]

4. Divide by 4:
\[
x = 5
\]

### Summary of Solutions

- \( a = 6 \)
- \( r = -7 \)
- \( x = 5 \)

Let me know if you need further assistance!