What Value Of $d$ Is A Solution To This Equation?$8d = 48$A. $ D = 6 D = 6 D = 6 [/tex] B. $d = 8$

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Solving for d in the Equation 8d = 48

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving for the variable d in the equation 8d = 48. We will explore the steps involved in solving this equation and determine the correct value of d.

Understanding the Equation

The given equation is 8d = 48. This equation states that 8 times the value of d is equal to 48. To solve for d, we need to isolate the variable d on one side of the equation.

Step 1: Divide Both Sides by 8

To isolate d, we need to get rid of the coefficient 8 that is being multiplied by d. We can do this by dividing both sides of the equation by 8.

8d = 48

Dividing both sides by 8 gives us:

d = 48/8

Simplifying the Equation

Now that we have divided both sides by 8, we can simplify the equation by performing the division.

d = 6

Based on the steps we have taken, we can conclude that the value of d that satisfies the equation 8d = 48 is d = 6.

Why is d = 6 the Correct Answer?

To verify that d = 6 is the correct answer, we can substitute this value back into the original equation and check if it holds true.

8d = 48

Substituting d = 6 into the equation gives us:

8(6) = 48

48 = 48

Since the equation holds true, we can confirm that d = 6 is indeed the correct answer.

Comparison with Option B

Option B states that d = 8 is a solution to the equation 8d = 48. However, if we substitute d = 8 into the equation, we get:

8(8) = 64

64 ≠ 48

Since the equation does not hold true, we can conclude that d = 8 is not a solution to the equation 8d = 48.

In conclusion, the value of d that satisfies the equation 8d = 48 is d = 6. This is the correct answer based on the steps we have taken to solve the equation. We have also compared this answer with option B and found that d = 8 is not a solution to the equation.

The final answer is d = 6.
Frequently Asked Questions (FAQs) about Solving for d in the Equation 8d = 48

In our previous article, we solved for the variable d in the equation 8d = 48. We found that the value of d that satisfies the equation is d = 6. In this article, we will answer some frequently asked questions (FAQs) about solving for d in the equation 8d = 48.

Q: What is the equation 8d = 48?

A: The equation 8d = 48 is a linear equation that states that 8 times the value of d is equal to 48.

Q: How do I solve for d in the equation 8d = 48?

A: To solve for d, you need to isolate the variable d on one side of the equation. You can do this by dividing both sides of the equation by 8.

Q: What is the value of d that satisfies the equation 8d = 48?

A: The value of d that satisfies the equation 8d = 48 is d = 6.

Q: Why is d = 6 the correct answer?

A: d = 6 is the correct answer because when you substitute this value back into the original equation, it holds true. In other words, 8(6) = 48.

Q: What happens if I substitute d = 8 into the equation 8d = 48?

A: If you substitute d = 8 into the equation 8d = 48, you get 8(8) = 64, which is not equal to 48. Therefore, d = 8 is not a solution to the equation 8d = 48.

Q: Can I use other methods to solve for d in the equation 8d = 48?

A: Yes, you can use other methods to solve for d in the equation 8d = 48. For example, you can use the inverse operation of multiplication, which is division, to isolate d.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division. In other words, if you multiply two numbers together, you can divide the product by one of the numbers to get the other number.

Q: Can I use algebraic manipulations to solve for d in the equation 8d = 48?

A: Yes, you can use algebraic manipulations to solve for d in the equation 8d = 48. For example, you can add or subtract the same value to both sides of the equation to isolate d.

Q: What are some common mistakes to avoid when solving for d in the equation 8d = 48?

A: Some common mistakes to avoid when solving for d in the equation 8d = 48 include:

  • Not isolating the variable d on one side of the equation
  • Not using the correct inverse operation (division) to isolate d
  • Not checking the solution by substituting it back into the original equation

In conclusion, solving for d in the equation 8d = 48 is a straightforward process that involves isolating the variable d on one side of the equation. We have answered some frequently asked questions (FAQs) about solving for d in the equation 8d = 48 and provided some tips and common mistakes to avoid.

The final answer is d = 6.