Certainly! We need to solve the equation [tex]\(3x - 7 = 7x - 14\)[/tex] and find the value of [tex]\(x\)[/tex]. Let's go through the steps in detail.
1. Write the given equation:
[tex]\[
3x - 7 = 7x - 14
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side and the constants to the other side:
[tex]\[
3x - 7 - 7x = -14
\][/tex]
3. Combine like terms:
[tex]\[
3x - 7x - 7 = -14
\][/tex]
This simplifies to:
[tex]\[
-4x - 7 = -14
\][/tex]
4. Add 7 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
-4x - 7 + 7 = -14 + 7
\][/tex]
Simplifying the equation, we get:
[tex]\[
-4x = -7
\][/tex]
5. Divide by [tex]\(-4\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-7}{-4}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
x = \frac{7}{4}
\][/tex]
So, the solution is [tex]\(x = \frac{7}{4}\)[/tex], which is equivalent to [tex]\(1.75\)[/tex].
Therefore, the correct answer from the given options is:
[tex]\[
x = \frac{7}{4}
\][/tex]
