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Chapter 3: Problem 57

Solve the equation. $$100=5 k$$

Short Answer

Expert verified
k = 20

Step by step solution

01

Write down the equation

Start with the given equation: 100 = 5k
02

Isolate the variable

To solve for the variable \( k \), divide both sides of the equation by 5. This will help to isolate \( k \). \[ \frac{100}{5} = \frac{5k}{5} \]
03

Simplify

Simplify both sides of the equation: \[ 20 = k \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
In order to solve the equation given in the problem, the main goal is to find the value of the variable, which in this case is \( k \). This is done by isolating \( k \) on one side of the equation.
Start with the given equation:
100 = 5k
To isolate the variable \( k \), we need to undo the multiplication of \( k \) by 5.
To do this, we divide both sides of the equation by 5, because the opposite operation of multiplication is division.
  • Divide both sides by 5:
    \( \frac{100}{5} = \frac{5k}{5} \)
Now we have successfully isolated \( k \), as we will see in the following section.
Basic Arithmetic
Now that we have set up our equation so that \( k \) is on one side and numbers are on the other, it's time to use basic arithmetic to simplify it further.
Use division to divide 100 by 5:

    \( \frac{100}{5} = 20 \)

This gives us:
20 = k Remember, basic arithmetic operations such as addition, subtraction, multiplication, and division are fundamental tools, necessary to solving equations. Make sure you perform these operations correctly to find the right solution.
Simplifying Equations
Simplifying an equation means making it as simple as possible, which usually allows you to clearly see the value of the variable that you're solving for.
In this example, once you have performed the division, the equation becomes:
20 = k
By carrying out the division, we have simplified the equation and isolated the variable completely.

    This tells us directly that \( k = 20 \).

Simplified equations are easier to understand and work with, so always strive to reduce complicated equations to their simplest form.

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