To solve the equation [tex]\(5kx + 6 = 7kx\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Write down the given equation:
[tex]\[ 5kx + 6 = 7kx \][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
To do this, subtract [tex]\(5kx\)[/tex] from both sides:
[tex]\[ 6 = 7kx - 5kx \][/tex]
3. Simplify the equation:
Combine like terms on the right-hand side:
[tex]\[ 6 = (7k - 5k)x \][/tex]
[tex]\[ 6 = 2kx \][/tex]
4. Isolate [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(2k\)[/tex]:
[tex]\[ x = \frac{6}{2k} \][/tex]
5. Simplify the fraction:
[tex]\[ x = \frac{6}{2k} = \frac{3}{k} \][/tex]
Therefore, the solution to the equation [tex]\(5kx + 6 = 7kx\)[/tex] is [tex]\(x = \frac{3}{k}\)[/tex].
Looking at the provided options:
A. [tex]\(x = -\frac{2}{k}\)[/tex]
B. [tex]\(x = -\frac{3}{k}\)[/tex]
C. [tex]\(x = \frac{3}{k}\)[/tex]
D. [tex]\(x = \frac{2}{k}\)[/tex]
The correct answer is:
C. [tex]\(x = \frac{3}{k}\)[/tex]
