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Chapter 2: Problem 37

Solve each equation. $$ \frac{k}{7}=0 $$

Short Answer

Expert verified
The solution is \( k = 0 \).

Step by step solution

01

Understand the Equation

The equation given is \( \frac{k}{7} = 0 \). This means that when \( k \) is divided by 7, the result is 0. To solve for \( k \), we need to find a value for \( k \) that satisfies this condition.
02

Isolate Variable \( k \)

To find \( k \), we must cancel out the division by 7. We do this by performing the inverse operation, which is multiplication, on both sides of the equation. Multiply both sides by 7: \[ 7 \times \frac{k}{7} = 7 \times 0 \]
03

Simplify Both Sides

On the left side, multiplying by 7 will cancel out the division by 7: \[ k = 0 \] On the right side, multiplying 0 by 7 gives 0. Thus, the equation simplifies to \( k = 0 \).

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Key Concepts

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

Solving Equations
When faced with algebraic equations such as \( \frac{k}{7} = 0 \), our goal is to find the unknown variable, in this case, \( k \). Solving equations requires logical steps to isolate the variable on one side of the equation.
For the equation \( \frac{k}{7} = 0 \), we want \( k \) to be by itself. This involves moving other numbers or operations that are with \( k \) to the other side of the equation. Only then can we determine the actual value of \( k \).
  • Ensure the equation is balanced by performing the same operation on both sides.
  • Use basic arithmetic operations, such as addition, subtraction, multiplication, and division, to achieve this balance.
  • The ultimate goal is to have the term with our variable, \( k \), alone.

Let's break down how to solve it in simple terms in the following sections.
Inverse Operations
Inverse operations are mathematical operations that undo each other, like addition with subtraction and multiplication with division. Understanding inverse operations is crucial to solving equations.
For the problem \( \frac{k}{7} = 0 \), we use inverse operations to isolate \( k \).
  • Since \( k \) is divided by 7, the inverse operation is multiplication.
  • We multiply both sides of the equation by 7 to cancel out the division.

This process helps us solve the equation effectively by eliminating the fraction and leaving us with \( k \) by itself. This use of inverse operations ensures that the equation remains balanced.
Division in Equations
When dealing with division in algebraic equations, it's important to tackle it correctly to find a solution. In the equation \( \frac{k}{7} = 0 \), the division suggests that \( k \) is divided by 7 and gives a result of 0.
To remove the division, consider the following steps:
  • The term \( \frac{k}{7} \) indicates that 7 is used to divide \( k \).
  • By applying the inverse operation, multiplying both sides by 7, we negate the division.

The action of \( 7 \times \frac{k}{7} \) simplifies to \( k \) because multiplying and dividing by the same number cancels both out. Consequently, \( k = 0 \) emerges as the solved equation. This approach is consistent when dealing with variables and divisions in equations.

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