What's the Letters number

Question

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!