Sure, let's solve the equation step-by-step:
The given equation is:
[tex]\[ 3(2x - 4) = x + 12 \][/tex]
1. Distribute the 3 on the left side:
- Multiply each term inside the parentheses by 3.
[tex]\[ 3 \cdot 2x - 3 \cdot 4 = 6x - 12 \][/tex]
So the equation now becomes:
[tex]\[ 6x - 12 = x + 12 \][/tex]
2. Rearrange the equation to move all [tex]\( x \)[/tex]-terms to one side and constants to the other side:
- First, subtract [tex]\( x \)[/tex] from both sides to move all [tex]\( x \)[/tex]-terms to one side:
[tex]\[ 6x - x - 12 = 12 \][/tex]
This simplifies to:
[tex]\[ 5x - 12 = 12 \][/tex]
- Next, add 12 to both sides to move the constants to one side:
[tex]\[ 5x - 12 + 12 = 12 + 12 \][/tex]
This simplifies to:
[tex]\[ 5x = 24 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Divide both sides of the equation by 5 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{5} \][/tex]
4. Simplify the fraction (if possible):
- In this case, [tex]\( \frac{24}{5} \)[/tex] is already in its simplest form.
Therefore, the simplified value of [tex]\( x \)[/tex] is:
[tex]\[ x = \frac{24}{5} \][/tex]
