Solve 5x +14 = k For x.
The correct answer and explanation is:
Correct Answer:
To solve the equation:
5x + 14 = k, solve for x.
Step 1: Subtract 14 from both sides
5x + 14 − 14 = k − 14
So, 5x = k − 14
Step 2: Divide both sides by 5
x = (k − 14)/5
Final Answer:
x = (k − 14)/5
Explanation (300 words):
The goal in this equation is to isolate the variable x on one side of the equation. The given equation is 5x + 14 = k. It is a linear equation that follows the form of ax + b = c, where a = 5, b = 14, and c = k. Solving such an equation involves performing inverse operations to eliminate the constants and coefficients surrounding the variable.
Start by removing the number added to the term containing x. In this case, 14 is added to 5x. The inverse of addition is subtraction, so subtract 14 from both sides of the equation. This keeps the equation balanced and simplifies the left side to just the term 5x. The right side becomes k − 14.
Now you are left with 5x = k − 14. The next step is to remove the coefficient 5 that is multiplied by x. The inverse operation of multiplication is division. So divide both sides of the equation by 5. This step isolates x completely and gives the expression x = (k − 14)/5.
This solution is considered general because k can be any constant or variable expression. This form is useful in algebra when working with unknown quantities or when graphing linear functions. It shows that x depends directly on the value of k and changes as k changes. This expression helps in understanding the relationship between the variable x and any given value assigned to k.