Let us solve the given equation step by step.
The given equation is:
[tex]\[
2(7x + 4) = 4x - 6(2 - x) + 7
\][/tex]
First, distribute the constants on both sides of the equation.
For the left side:
[tex]\[
2(7x + 4) = 2 \cdot 7x + 2 \cdot 4 = 14x + 8
\][/tex]
For the right side:
[tex]\[
4x - 6(2 - x) + 7 = 4x - 6 \cdot 2 + 6 \cdot x + 7 = 4x - 12 + 6x + 7 = 10x - 5
\][/tex]
Now, the equation is simplified to:
[tex]\[
14x + 8 = 10x - 5
\][/tex]
Next, combine like terms by moving all terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side.
Subtract [tex]\( 10x \)[/tex] from both sides:
[tex]\[
14x - 10x + 8 = -5
\][/tex]
Simplify it to:
[tex]\[
4x + 8 = -5
\][/tex]
Subtract 8 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
4x = -5 - 8
\][/tex]
Simplify it further:
[tex]\[
4x = -13
\][/tex]
Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{-13}{4}
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = -\frac{13}{4}
\][/tex]
The correct choice is:
B. [tex]\( x = -\frac{13}{4} \)[/tex]
