Problem 93
Question
$$ \text { Solve: } 800=5 k $$
Step-by-Step Solution
Verified Answer
The value of \(k\) is 160.
1Step 1 - Isolate the Variable
To find the value of the variable \(k\), we need to isolate it on one side of the equation. The given equation is \(800 = 5k\).
2Step 2 - Divide Both Sides by 5
To isolate \(k\), divide both sides of the equation by 5. This gives us \(k = \frac{800}{5}\).
3Step 3 - Simplify the Right-Hand Side
Perform the division to simplify the right-hand side of the equation: \(k = 160\).
Key Concepts
Isolate the VariableDivision Property of EqualitySimplification
Isolate the Variable
In solving linear equations, the first step is often to isolate the variable. This simply means getting the variable by itself on one side of the equation.
For example, let's consider our equation: \( 800 = 5k \).
Here, we want to solve for \( k \). To do this, we need \( k \) to appear alone on one side of the equation, with no other coefficients or constants attached to it.
The 'isolate the variable' step helps us simplify the problem and makes it easier to find the solution.
For example, let's consider our equation: \( 800 = 5k \).
Here, we want to solve for \( k \). To do this, we need \( k \) to appear alone on one side of the equation, with no other coefficients or constants attached to it.
The 'isolate the variable' step helps us simplify the problem and makes it easier to find the solution.
Division Property of Equality
The division property of equality is used when the variable you are solving for is multiplied by a coefficient. This principle states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
In our problem, we started with \( 800 = 5k \).
To isolate \( k \), we divide both sides by 5:
It's important to always perform the same operation on both sides to maintain the balance of the equation.
In our problem, we started with \( 800 = 5k \).
To isolate \( k \), we divide both sides by 5:
- Left Side: \( \frac{800}{5} \)
- Right Side: \( \frac{5k}{5} \)
It's important to always perform the same operation on both sides to maintain the balance of the equation.
Simplification
Simplification is the process of performing mathematical operations to make an equation easier to understand and solve.
After dividing both sides in our equation by 5, we got \( k = \frac{800}{5} \).
The final step is to perform the actual division to simplify this expression.
In this case, \( \frac{800}{5} = 160 \).
Thus, we conclude that \( k = 160 \).
Simplification helps to get the final, user-friendly answer that is easy to interpret.
After dividing both sides in our equation by 5, we got \( k = \frac{800}{5} \).
The final step is to perform the actual division to simplify this expression.
In this case, \( \frac{800}{5} = 160 \).
Thus, we conclude that \( k = 160 \).
Simplification helps to get the final, user-friendly answer that is easy to interpret.
Other exercises in this chapter
Problem 91
For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistak
View solution Problem 92
For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistak
View solution Problem 93
For exercises 91-94, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistak
View solution Problem 94
$$ \text { Solve: } 0.75=\frac{k}{60} $$
View solution