Question

5(a-2)=2+3a
-8(-5a+7)=7(7r+1)
x-29=-3(3+x)

Answer 1

To solve the equations, we'll start with each one individually.

### 1. Solve the equation \( 5(a - 2) = 2 + 3a \)

First, distribute the left side:

\[
5a - 10 = 2 + 3a
\]

Next, subtract \( 3a \) from both sides:

\[
5a - 3a - 10 = 2
\]

This simplifies to:

\[
2a - 10 = 2
\]

Now, add 10 to both sides:

\[
2a = 12
\]

Now divide both sides by 2:

\[
a = 6
\]

### 2. Solve the equation \( -8(-5a + 7) = 7(7r + 1) \)

Distribute on both sides:

\[
40a - 56 = 49r + 7
\]

Now, let's isolate terms involving \( a \) and \( r \). Add 56 to both sides:

\[
40a = 49r + 63
\]

This can also be expressed as:

\[
40a - 49r = 63
\]

This is a linear equation with two variables, so we cannot solve for specific values of \( a \) or \( r \) without additional information.

### 3. Solve the equation \( x - 29 = -3(3 + x) \)

First, distribute on the right:

\[
x - 29 = -9 - 3x
\]

Now, add \( 3x \) to both sides:

\[
x + 3x - 29 = -9
\]

This simplifies to:

\[
4x - 29 = -9
\]

Next, add 29 to both sides:

\[
4x = 20
\]

Now, divide both sides by 4:

\[
x = 5
\]

### Summarizing the solutions:
1. \( a = 6 \)
2. \( 40a - 49r = 63 \) (relationship between \( a \) and \( r \))
3. \( x = 5 \)