Alright! Let's go through the process of solving the given equation step-by-step:
The equation given to us is:
[tex]\[ 3x + 7 = 2x + 15 \][/tex]
Our goal is to solve for the variable [tex]\( x \)[/tex]. We will start by isolating [tex]\( x \)[/tex].
### Step 1: Move terms involving [tex]\( x \)[/tex] to one side of the equation
First, we should eliminate [tex]\( 2x \)[/tex] from the right side by subtracting [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 3x + 7 - 2x = 2x + 15 - 2x \][/tex]
Which simplifies to:
[tex]\[ x + 7 = 15 \][/tex]
### Step 2: Simplify the equation
Now, we want to isolate [tex]\( x \)[/tex] further by getting rid of the constant term on the left side. We do this by subtracting 7 from both sides:
[tex]\[ x + 7 - 7 = 15 - 7 \][/tex]
Which simplifies to:
[tex]\[ x = 8 \][/tex]
### Step 3: Check the solution
We need to verify that [tex]\( x = 8 \)[/tex] satisfies the original equation. Substitute [tex]\( x = 8 \)[/tex] back into the original equation:
[tex]\[ 3(8) + 7 = 2(8) + 15 \][/tex]
Calculate each side:
[tex]\[ 24 + 7 = 16 + 15 \][/tex]
[tex]\[ 31 = 31 \][/tex]
Since both sides of the equation are equal when [tex]\( x = 8 \)[/tex], our solution is verified.
Hence, the solution set for the equation is:
A. [tex]\(\{ 8 \}\)[/tex]
