To solve the equation [tex]\(2.5(6x - 4) = 10 + 4(1.5 + 0.5x)\)[/tex], we need to carefully follow each step to isolate the variable [tex]\(x\)[/tex]. Here's a detailed, step-by-step solution:
1. Distribute values inside the parentheses:
[tex]\[
2.5(6x - 4) = 10 + 4(1.5 + 0.5x)
\][/tex]
Distribute [tex]\(2.5\)[/tex] on the left-hand side and [tex]\(4\)[/tex] on the right-hand side:
[tex]\[
2.5 \cdot 6x - 2.5 \cdot 4 = 10 + 4 \cdot 1.5 + 4 \cdot 0.5x
\][/tex]
Simplifying these terms, we get:
[tex]\[
15x - 10 = 10 + 6 + 2x
\][/tex]
2. Combine like terms on the right-hand side:
[tex]\[
15x - 10 = 16 + 2x
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we'll move the [tex]\(2x\)[/tex] term to the left-hand side and the constant term [tex]\(-10\)[/tex] to the right-hand side. Subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
15x - 2x - 10 = 16
\][/tex]
This simplifies to:
[tex]\[
13x - 10 = 16
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add [tex]\(10\)[/tex] to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
13x = 26
\][/tex]
5. Divide by the coefficient of [tex]\(x\)[/tex] to find its value:
[tex]\[
x = \frac{26}{13}
\][/tex]
[tex]\[
x = 2
\][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\(2\)[/tex].
Among the given answer choices:
[tex]\[
\boxed{2}
\][/tex]
