Write And Solve The Equation, Then Check Your Answer.Four Times A Number Is Thirty-two. Which Statements Are True? Check All That Apply.- This Is A Division Problem.- This Is A Multiplication Problem.- The Correct Equation Is

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Understanding the Problem

In this article, we will explore the concept of solving equations and check our answers. We will use a specific problem to demonstrate the process: "Four times a number is thirty-two." We will analyze the statements provided and determine which ones are true.

Breaking Down the Problem

Let's break down the problem into smaller parts. We are given the statement "Four times a number is thirty-two." This can be translated into a mathematical equation as:

4x = 32

where x is the unknown number.

Checking the Statements

Now, let's examine the statements provided and determine which ones are true.

Statement 1: This is a division problem.

  • Analysis: A division problem involves dividing one number by another to find the quotient. In this case, we are trying to find the value of x by dividing 32 by 4. Therefore, this statement is TRUE.

Statement 2: This is a multiplication problem.

  • Analysis: A multiplication problem involves multiplying one number by another to find the product. In this case, we are trying to find the value of x by multiplying 4 by x to get 32. Therefore, this statement is TRUE.

Statement 3: The correct equation is 4x = 32.

  • Analysis: The correct equation is indeed 4x = 32. This equation represents the problem statement "Four times a number is thirty-two." Therefore, this statement is TRUE.

Solving the Equation

Now that we have analyzed the statements, let's solve the equation 4x = 32.

Step 1: Divide both sides by 4

To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 4.

4x / 4 = 32 / 4

x = 8

Step 2: Check the answer

Now that we have solved for x, let's check our answer by plugging it back into the original equation.

4(8) = 32

32 = 32

Our answer is correct!

Conclusion

In this article, we explored the concept of solving equations and checked our answers. We used a specific problem to demonstrate the process and analyzed the statements provided to determine which ones are true. We also solved the equation 4x = 32 and checked our answer to ensure it is correct. By following these steps, we can confidently solve equations and check our answers.

Key Takeaways

  • A division problem involves dividing one number by another to find the quotient.
  • A multiplication problem involves multiplying one number by another to find the product.
  • The correct equation is indeed 4x = 32.
  • To solve for x, we need to isolate x on one side of the equation by dividing both sides by 4.
  • We can check our answer by plugging it back into the original equation.

Additional Resources

For more information on solving equations and checking answers, please refer to the following resources:

  • Khan Academy: Solving Equations
  • Mathway: Solving Equations
  • Wolfram Alpha: Solving Equations

Frequently Asked Questions

In this article, we will address some of the most common questions related to solving equations and checking answers. We will provide detailed explanations and examples to help you understand the concepts better.

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS is the expression on the left side of the equation, and the RHS is the expression on the right side.

Example: 2x + 3 = 5

In this equation, the LHS is 2x + 3, and the RHS is 5.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Example: Linear equation: 2x + 3 = 5 Quadratic equation: x^2 + 4x + 4 = 0

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable (usually x) on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Example: Solve the equation 2x + 3 = 5

Subtract 3 from both sides: 2x = 2 Divide both sides by 2: x = 1

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to find the values of the variable (usually x) that satisfy the equation. You can do this by factoring the equation, using the quadratic formula, or completing the square.

Example: Solve the equation x^2 + 4x + 4 = 0

Factor the equation: (x + 2)(x + 2) = 0 Solve for x: x + 2 = 0, x = -2

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Example: Evaluate the expression 2 + 3 × 4 - 5

Using the order of operations, we get:

  1. Evaluate the expression inside the parentheses: 3 × 4 = 12
  2. Evaluate the multiplication operation: 2 + 12 = 14
  3. Evaluate the addition and subtraction operations from left to right: 14 - 5 = 9

Q: How do I check my answer?

A: To check your answer, plug it back into the original equation and evaluate it. If the equation is true, then your answer is correct.

Example: Check the answer x = 1 for the equation 2x + 3 = 5

Plug x = 1 into the equation: 2(1) + 3 = 5 Evaluate the equation: 2 + 3 = 5

Since the equation is true, the answer x = 1 is correct.

Conclusion

In this article, we addressed some of the most common questions related to solving equations and checking answers. We provided detailed explanations and examples to help you understand the concepts better. By following these guidelines and practicing solving equations, you can become more confident in your math skills and tackle more complex problems.

Key Takeaways

  • An equation is a statement that expresses the equality of two mathematical expressions.
  • A linear equation is an equation in which the highest power of the variable is 1.
  • A quadratic equation is an equation in which the highest power of the variable is 2.
  • To solve a linear equation, isolate the variable on one side of the equation.
  • To solve a quadratic equation, find the values of the variable that satisfy the equation.
  • The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression.
  • To check your answer, plug it back into the original equation and evaluate it.

Additional Resources

For more information on solving equations and checking answers, please refer to the following resources:

  • Khan Academy: Solving Equations
  • Mathway: Solving Equations
  • Wolfram Alpha: Solving Equations

By following these resources and practicing solving equations, you can become more confident in your math skills and tackle more complex problems.