What Is The Solution Of 2 X + 4 = 16 \sqrt{2x+4}=16 2 X + 4 ​ = 16 ?A. X = 6 X=6 X = 6 B. X = 72 X=72 X = 72 C. X = 126 X=126 X = 126 D. No Solution

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Introduction

Solving equations involving square roots can be a bit tricky, but with the right approach, it's definitely manageable. In this article, we'll focus on solving the equation $\sqrt{2x+4}=16$ and explore the different steps involved in finding the solution.

Understanding the Equation

The given equation is $\sqrt{2x+4}=16$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The first step is to square both sides of the equation to eliminate the square root.

Squaring Both Sides

When we square both sides of the equation, we get:

$$\left(\sqrt{2x+4}\right)^2 = 16^2$$

This simplifies to:

$$2x+4 = 256$$

Simplifying the Equation

Now, we need to isolate the variable $x$ on one side of the equation. To do this, we'll subtract 4 from both sides of the equation:

$$2x = 256 - 4$$

This simplifies to:

$$2x = 252$$

Solving for $x$

Finally, we'll divide both sides of the equation by 2 to solve for $x$:

$$x = \frac{252}{2}$$

This simplifies to:

$$x = 126$$

Conclusion

Therefore, the solution to the equation $\sqrt{2x+4}=16$ is $x=126$. This means that when we substitute $x=126$ into the original equation, the equation holds true.

Discussion

Let's take a closer look at the steps involved in solving the equation. We started by squaring both sides of the equation to eliminate the square root. This is a common technique used to solve equations involving square roots. We then simplified the equation by subtracting 4 from both sides and dividing both sides by 2 to solve for $x$.

Alternative Solutions

It's worth noting that there are no alternative solutions to this equation. The equation has a unique solution, which is $x=126$. This means that there is no other value of $x$ that satisfies the equation.

Final Thoughts

Solving equations involving square roots can be a bit challenging, but with the right approach, it's definitely manageable. By following the steps outlined in this article, you should be able to solve equations involving square roots with ease.

Frequently Asked Questions

• What is the solution to the equation $\sqrt{2x+4}=16$?
• How do you solve equations involving square roots?
• What is the first step in solving an equation involving a square root?

Answers

• The solution to the equation $\sqrt{2x+4}=16$ is $x=126$.
• To solve equations involving square roots, you need to square both sides of the equation to eliminate the square root.
• The first step in solving an equation involving a square root is to square both sides of the equation.

Conclusion

In conclusion, solving the equation $\sqrt{2x+4}=16$ involves squaring both sides of the equation to eliminate the square root, simplifying the equation, and solving for $x$. The solution to the equation is $x=126$, and there are no alternative solutions. By following the steps outlined in this article, you should be able to solve equations involving square roots with ease.

Introduction

Solving equations involving square roots can be a bit challenging, but with the right approach, it's definitely manageable. In this article, we'll answer some frequently asked questions about solving equations involving square roots.

Q: What is the solution to the equation $\sqrt{2x+4}=16$?

A: The solution to the equation $\sqrt{2x+4}=16$ is $x=126$. This means that when we substitute $x=126$ into the original equation, the equation holds true.

Q: How do you solve equations involving square roots?

A: To solve equations involving square roots, you need to square both sides of the equation to eliminate the square root. This is a common technique used to solve equations involving square roots.

Q: What is the first step in solving an equation involving a square root?

A: The first step in solving an equation involving a square root is to square both sides of the equation. This will eliminate the square root and allow you to simplify the equation.

Q: Can you give an example of an equation involving a square root that has no solution?

A: Yes, consider the equation $\sqrt{x+1}=-3$. When we square both sides of the equation, we get:

$$x+1 = 9$$

Subtracting 1 from both sides gives:

$$x = 8$$

However, when we substitute $x=8$ into the original equation, we get:

$$\sqrt{8+1} = \sqrt{9} = 3$$

This is not equal to -3, so the equation has no solution.

Q: How do you know if an equation involving a square root has a solution or not?

A: To determine if an equation involving a square root has a solution or not, you need to check if the expression inside the square root is non-negative. If it is, then the equation has a solution. If it's not, then the equation has no solution.

Q: Can you give an example of an equation involving a square root that has multiple solutions?

A: Yes, consider the equation $\sqrt{x-1} = \pm 3$. When we square both sides of the equation, we get:

$$x-1 = 9$$

or

$$x-1 = -9$$

Adding 1 to both sides gives:

$$x = 10$$

or

$$x = -8$$

Both of these values satisfy the original equation, so the equation has two solutions.

Q: How do you know if an equation involving a square root has multiple solutions or not?

A: To determine if an equation involving a square root has multiple solutions or not, you need to check if the expression inside the square root is non-negative. If it is, then the equation has multiple solutions. If it's not, then the equation has no solution.

Q: Can you give an example of an equation involving a square root that has a negative value inside the square root?

A: Yes, consider the equation $\sqrt{x-1} = 3$. When we square both sides of the equation, we get:

$$x-1 = 9$$

Adding 1 to both sides gives:

$$x = 10$$

However, when we substitute $x=10$ into the original equation, we get:

$$\sqrt{10-1} = \sqrt{9} = 3$$

This is not a negative value, so the equation has a solution.

Q: How do you know if an equation involving a square root has a negative value inside the square root or not?

A: To determine if an equation involving a square root has a negative value inside the square root or not, you need to check if the expression inside the square root is less than 0. If it is, then the equation has no solution. If it's not, then the equation has a solution.

Conclusion

In conclusion, solving equations involving square roots can be a bit challenging, but with the right approach, it's definitely manageable. By following the steps outlined in this article, you should be able to solve equations involving square roots with ease.