Question

solve and explain:

3x + 2 ( 5x - 3) = 7

Answer 1

To solve the equation \(3x + 2(5x - 3) = 7\), we will follow these steps:

### Step 1: Distribute the \(2\)
First, we need to distribute the \(2\) across the terms inside the parentheses:

\[
2(5x - 3) = 2 \cdot 5x - 2 \cdot 3 = 10x - 6
\]

### Step 2: Substitute back into the equation
Now we substitute \(10x - 6\) back into the original equation:

\[
3x + 10x - 6 = 7
\]

### Step 3: Combine like terms
Next, we combine the \(3x\) and \(10x\):

\[
(3x + 10x) - 6 = 7 \implies 13x - 6 = 7
\]

### Step 4: Isolate the variable \(x\)
Now, to solve for \(x\), we add \(6\) to both sides of the equation:

\[
13x - 6 + 6 = 7 + 6 \implies 13x = 13
\]

### Step 5: Divide by \(13\)
Finally, we divide both sides by \(13\):

\[
x = \frac{13}{13} = 1
\]

### Conclusion
The solution to the equation \(3x + 2(5x - 3) = 7\) is:

\[
\boxed{1}
\]

### Verification
To verify, we can substitute \(x = 1\) back into the original equation:

\[
3(1) + 2(5(1) - 3) = 3 + 2(5 - 3) = 3 + 2(2) = 3 + 4 = 7
\]

Since both sides equal \(7\), our solution \(x = 1\) is correct.