Is $k=4$ a solution of $4 k+7=7 k-1$?
Answer (2)
Substitute k = 4 into the left-hand side (LHS) of the equation: 4 k + 7 = 4 ( 4 ) + 7 = 23 .
Substitute k = 4 into the right-hand side (RHS) of the equation: 7 k − 1 = 7 ( 4 ) − 1 = 27 .
Compare the LHS and RHS: 23 = 27 .
Conclude that k = 4 is not a solution: F a l se .
Explanation
Problem Analysis We are given the equation 4 k + 7 = 7 k − 1 and we want to determine if k = 4 is a solution. To do this, we will substitute k = 4 into both sides of the equation and check if they are equal.
Calculate LHS First, we substitute k = 4 into the left-hand side (LHS) of the equation: 4 k + 7 . 4 k + 7 = 4 ( 4 ) + 7 = 16 + 7 = 23
Calculate RHS Next, we substitute k = 4 into the right-hand side (RHS) of the equation: 7 k − 1 . 7 k − 1 = 7 ( 4 ) − 1 = 28 − 1 = 27
Compare LHS and RHS Now we compare the LHS and RHS. We found that when k = 4 , the LHS is 23 and the RHS is 27. Since 23 e q 27 , k = 4 is not a solution to the equation 4 k + 7 = 7 k − 1 .
Conclusion Therefore, k = 4 is not a solution to the equation 4 k + 7 = 7 k − 1 .
Examples
In real life, you might use this type of problem to check if a certain value satisfies a given condition, such as verifying if a specific input meets the requirements of a system or process. For example, if you have a formula that calculates the cost of a product based on the number of units produced, you can use this method to check if producing a certain number of units results in a desired cost. This is a fundamental concept in algebra and is used in various fields such as engineering, economics, and computer science.
We checked if k = 4 is a solution to the equation 4 k + 7 = 7 k − 1 by substituting k = 4 into both sides. The left-hand side evaluated to 23, while the right-hand side evaluated to 27, showing they are not equal. Thus, k = 4 is not a solution.
;
