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