What is the solution to this equation?

[tex]\[ 2(7x + 4) = 4x - 6(2 - x) + 7 \][/tex]

A. [tex]\[ x = -\frac{13}{16} \][/tex]

B. [tex]\[ x = -\frac{13}{4} \][/tex]

C. [tex]\[ x = -\frac{3}{16} \][/tex]

D. [tex]\[ x = -\frac{3}{4} \][/tex]



Answer :

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]