To solve the equation [tex]\(4(5x + 3) = 14x + 30\)[/tex], let's follow a step-by-step approach:
1. Expand the left side of the equation:
[tex]\(4(5x + 3)\)[/tex]
Distribute the [tex]\(4\)[/tex] across the terms inside the parentheses:
[tex]\(20x + 12\)[/tex]
Now the equation looks like:
[tex]\(20x + 12 = 14x + 30\)[/tex]
2. Move all the [tex]\(x\)[/tex] terms to one side:
To do this, subtract [tex]\(14x\)[/tex] from both sides of the equation:
[tex]\(20x + 12 - 14x = 14x + 30 - 14x\)[/tex]
This simplifies to:
[tex]\(6x + 12 = 30\)[/tex]
3. Move the constant terms to the other side:
To isolate the [tex]\(x\)[/tex] term, subtract [tex]\(12\)[/tex] from both sides:
[tex]\(6x + 12 - 12 = 30 - 12\)[/tex]
This simplifies to:
[tex]\(6x = 18\)[/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(6\)[/tex]:
[tex]\[
x = \frac{18}{6}
\][/tex]
Simplifying the fraction we get:
[tex]\(x = 3\)[/tex]
So, the solution to the equation [tex]\(4(5x + 3) = 14x + 30\)[/tex] is [tex]\(x = 3\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x = 3\)[/tex]
