To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 2(x-3) + 5x = 5(2x+6) \)[/tex], let’s solve it step-by-step:
1. Distribute and simplify both sides of the equation:
Starting with the left-hand side:
[tex]\[
2(x - 3) + 5x = 2x - 6 + 5x
\][/tex]
Simplifying:
[tex]\[
2x - 6 + 5x = 7x - 6
\][/tex]
Now, the right-hand side:
[tex]\[
5(2x + 6) = 10x + 30
\][/tex]
2. Set the simplified forms of both sides equal to each other:
[tex]\[
7x - 6 = 10x + 30
\][/tex]
3. Isolate [tex]\( x \)[/tex] by moving all [tex]\( x \)[/tex]-terms to one side and constant terms to the other side:
Begin by subtracting [tex]\( 7x \)[/tex] from both sides:
[tex]\[
7x - 6 - 7x = 10x + 30 - 7x
\][/tex]
Simplifying this gives:
[tex]\[
-6 = 3x + 30
\][/tex]
Next, subtract 30 from both sides:
[tex]\[
-6 - 30 = 3x
\][/tex]
Simplifying further:
[tex]\[
-36 = 3x
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{-36}{3}
\][/tex]
Simplifying this gives:
[tex]\[
x = -12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{-12}\)[/tex].
This corresponds to option A: -12.
