Solve 5x +14 = k For x.
The correct answer and explanation is:
Correct Answer:
To solve the equation 5x + 14 = k for x, follow these steps:
Step 1: Subtract 14 from both sides of the equation.
5x + 14 − 14 = k − 14
This simplifies to:
5x = k − 14
Step 2: Divide both sides by 5.
(5x) ÷ 5 = (k − 14) ÷ 5
This simplifies to:
x = (k − 14) / 5
Explanation (300 words):
Solving an equation means finding the value of the variable that makes the equation true. In the equation 5x + 14 = k, the goal is to isolate the variable x on one side of the equation so its value can be determined in terms of k.
Start by recognizing the operations performed on x. In this equation, x is first multiplied by 5, and then 14 is added. To isolate x, these operations must be reversed using the order of operations in reverse (also called inverse operations).
The first step is to remove the number added to 5x, which is 14. Subtracting 14 from both sides keeps the equation balanced and simplifies the left-hand side. After subtracting, the equation becomes 5x = k − 14. Now, x is still multiplied by 5. To undo this multiplication, divide both sides by 5. This step isolates x completely.
The final expression, x = (k − 14) / 5, is the solution. It shows that x depends on the value of k, and it can be calculated for any specific value of k.
This solution technique demonstrates how algebraic manipulation helps to isolate variables in linear equations. It is especially useful when working with formulas or expressions that need to be rearranged to solve for a specific unknown. This type of problem is common in algebra and helps develop skills that are essential for more advanced mathematical problem-solving.