3k-1=7k+2 is a mathematical equation that involves solving for the value of ‘k’. Let’s break it down step by step:
- Start by isolating the variable term ‘k’ on one side of the equation. To do this, we can move the constant terms to the other side. We can achieve this by adding 1 to both sides of the equation:3k – 1 + 1 = 7k + 2 + 1Simplifying the equation gives us:3k = 7k + 3
- Now, let’s isolate the ‘k’ term by subtracting 7k from both sides of the equation:3k – 7k = 7k – 7k + 3Simplifying the equation further gives us:-4k = 3
- To find the value of ‘k’, we need to get rid of the coefficient -4 in front of the ‘k’. We can achieve this by dividing both sides of the equation by -4:(-4k) / -4 = 3 / -4Simplifying the equation yields:k = -3/4
Therefore, the solution to the equation 3k-1=7k+2 is k = -3/4.
Let’s substitute the value of k back into the original equation to verify our solution:
When k = -3/4, the equation becomes:
3(-3/4) – 1 = 7(-3/4) + 2
Simplifying the equation gives us:
-9/4 – 1 = -21/4 + 2
-9/4 – 4/4 = -21/4 + 8/4
-13/4 = -13/4
The equation holds true, which confirms that k = -3/4 is the correct solution.
I hope this explanation clarifies the concept for you. If you have any further questions, feel free to ask!