Let's solve the given equation step by step:
The given equation is:
[tex]\[ 9 - 4x = 3x - 4 \][/tex]
First, we want to move all the terms involving [tex]\(x\)[/tex] to one side of the equation, and the constant terms to the other side. We can start by adding [tex]\(4x\)[/tex] to both sides to eliminate the [tex]\(-4x\)[/tex] on the left side:
[tex]\[ 9 = 3x + 4x - 4 \][/tex]
[tex]\[ 9 = 7x - 4 \][/tex]
Next, we add 4 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 9 + 4 = 7x \][/tex]
[tex]\[ 13 = 7x \][/tex]
To solve for [tex]\(x\)[/tex], we divide both sides by 7:
[tex]\[ x = \frac{13}{7} \][/tex]
So, the solution to the equation is:
[tex]\[ x = \frac{13}{7} \][/tex]
Now, let's compare this solution with the choices given:
A. [tex]\( x = \frac{13}{7} \)[/tex]
B. [tex]\( x = 13 \)[/tex]
C. [tex]\( x = -\frac{13}{7} \)[/tex]
D. [tex]\( x = \frac{7}{13} \)[/tex]
The correct answer is:
A. [tex]\( x = \frac{13}{7} \)[/tex]
