To solve the equation [tex]\( 3x - 7 = 7x - 14 \)[/tex], follow these steps:
1. Rewrite the equation to move all the terms involving [tex]\( x \)[/tex] to one side and the constants to the other side. Start by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]\[
3x - 7 - 3x = 7x - 14 - 3x
\][/tex]
Simplify this to:
[tex]\[
-7 = 4x - 14
\][/tex]
2. Next, isolate the term with [tex]\( x \)[/tex]. Add 14 to both sides to move the constants:
[tex]\[
-7 + 14 = 4x - 14 + 14
\][/tex]
Simplify this to:
[tex]\[
7 = 4x
\][/tex]
3. Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{7}{4}
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that solves the equation [tex]\( 3x - 7 = 7x - 14 \)[/tex] is:
[tex]\[
x = \frac{7}{4}
\][/tex]
This matches the option [tex]\( x = \frac{7}{4} \)[/tex] from the given choices.
