What Is The Value Of $k$? Show Your Work. (Hint: You Can Multiply By Something To Get Rid Of That Nasty Repeating Decimal!) Your Answer Is A Fraction! 5 4 ( 2 − K ) = 2 ( 3 K − 1 ) − 2 3 K \frac{5}{4}(2-k)=2(3k-1)-\frac{2}{3}k 4 5 ( 2 − K ) = 2 ( 3 K − 1 ) − 3 2 K
What is the Value of $k$?
In this article, we will explore the value of $k$ in a given mathematical equation. The equation provided is a linear equation that involves the variable $k$. Our goal is to isolate the variable $k$ and determine its value. We will use algebraic techniques to solve for $k$.
The given equation is:
Step 1: Multiply Both Sides by the Least Common Multiple (LCM)
To eliminate the fractions in the equation, we need to multiply both sides by the least common multiple (LCM) of the denominators. In this case, the LCM is 12.
Multiplying both sides by 12:
12 * (5/4)(2-k) = 12 * (2(3k-1) - (2/3)k)
Step 2: Simplify the Equation
After multiplying both sides by 12, we can simplify the equation by multiplying the fractions.
Simplifying the equation:
15(2-k) = 24(3k-1) - 8k
Step 3: Distribute the Numbers
Next, we need to distribute the numbers outside the parentheses to the terms inside.
Distributing the numbers:
30 - 15k = 72k - 24 - 8k
Step 4: Combine Like Terms
Now, we can combine the like terms on both sides of the equation.
Combining like terms:
30 - 15k = 64k - 24
Step 5: Add 15k to Both Sides
To isolate the variable $k$, we need to add 15k to both sides of the equation.
Adding 15k to both sides:
30 = 79k - 24
Step 6: Add 24 to Both Sides
Next, we need to add 24 to both sides of the equation.
Adding 24 to both sides:
54 = 79k
Step 7: Divide Both Sides by 79
Finally, we can divide both sides of the equation by 79 to solve for $k$.
Dividing both sides by 79:
k = 54/79
In this article, we have solved for the value of $k$ in a given mathematical equation. We used algebraic techniques to isolate the variable $k$ and determine its value. The final answer is a fraction: $\frac{54}{79}$.
Q&A: What is the Value of $k$?
In our previous article, we explored the value of $k$ in a given mathematical equation. We used algebraic techniques to isolate the variable $k$ and determine its value. In this article, we will answer some frequently asked questions related to the value of $k$.
Q: What is the final answer for the value of $k$?
A: The final answer for the value of $k$ is $\frac{54}{79}$.
Q: How did you eliminate the fractions in the equation?
A: To eliminate the fractions in the equation, we multiplied both sides by the least common multiple (LCM) of the denominators, which is 12.
Q: What is the least common multiple (LCM) of the denominators?
A: The least common multiple (LCM) of the denominators is 12.
Q: Why did you multiply both sides by 12?
A: We multiplied both sides by 12 to eliminate the fractions in the equation.
Q: What is the next step after multiplying both sides by 12?
A: After multiplying both sides by 12, we simplified the equation by multiplying the fractions.
Q: What is the simplified equation?
A: The simplified equation is $15(2-k) = 24(3k-1) - 8k$.
Q: How did you distribute the numbers in the equation?
A: We distributed the numbers outside the parentheses to the terms inside.
Q: What is the equation after distributing the numbers?
A: The equation after distributing the numbers is $30 - 15k = 72k - 24 - 8k$.
Q: How did you combine like terms in the equation?
A: We combined the like terms on both sides of the equation.
Q: What is the equation after combining like terms?
A: The equation after combining like terms is $30 - 15k = 64k - 24$.
Q: How did you add 15k to both sides of the equation?
A: We added 15k to both sides of the equation to isolate the variable $k$.
Q: What is the equation after adding 15k to both sides?
A: The equation after adding 15k to both sides is $30 = 79k - 24$.
Q: How did you add 24 to both sides of the equation?
A: We added 24 to both sides of the equation to isolate the variable $k$.
Q: What is the equation after adding 24 to both sides?
A: The equation after adding 24 to both sides is $54 = 79k$.
Q: How did you divide both sides by 79 to solve for $k$?
A: We divided both sides of the equation by 79 to solve for $k$.
Q: What is the final answer for the value of $k$?
A: The final answer for the value of $k$ is $\frac{54}{79}$.
In this article, we have answered some frequently asked questions related to the value of $k$. We hope that this Q&A article has provided additional clarity and understanding of the value of $k$. If you have any further questions, please don't hesitate to ask.