Let's tackle the mathematical problem step by step. The problem seems to involve solving an equation with two expressions.
First, let's identify and write down the given expressions:
1. \(\( 3x + 6 \)\)
2. \(\( 4x - 15 \)\)
To solve an equation, we typically need an equation format, which is an expression set equal to another expression. For example:
\(\[ 3x + 6 = 4x - 15 \]\)
Now, let's solve the equation \(\( 3x + 6 = 4x - 15 \)\):
### Step-by-Step Solution:
1. Set up the equation:
\(\[ 3x + 6 = 4x - 15 \]\)
2. Isolate the variable (x):
- To isolate \(\( x \)\), we need to get all the \(\( x \)\)-terms on one side of the equation and the constants on the other.
- First, we can subtract \(\( 3x \)\) from both sides to move the \(\( x \)\)-terms to one side:
\(\[ 3x + 6 - 3x = 4x - 15 - 3x \]\)
Simplifying this, we get:
\(\[ 6 = x - 15 \]\)
- Next, add 15 to both sides to move the constant to the other side:
\(\[ 6 + 15 = x - 15 + 15 \]\)
Simplifying this, we get:
\(\[ 21 = x \]\)
3. Verify the solution:
- Substitute \(\( x = 21 \)\) back into the original expressions to ensure both sides of the equation are equal.
- Left side: \(\( 3x + 6 \)\):
\(\[ 3(21) + 6 = 63 + 6 = 69 \]\)
- Right side: \(\( 4x - 15 \)\):
\(\[ 4(21) - 15 = 84 - 15 = 69 \]\)
- Since both sides are equal when \(\( x = 21 \)\), the solution is correct.
### Final Answer:
\(\[ x = 21 \]\)
