Distributing the Numbers Outside the Parentheses

Oct 13, 2025 by recoveryshake.com 145 views

Introduction

In this section, we will be solving the equation $4x + 2(2x - 3) = 8(x - 1)$ . To solve this equation, we will first need to simplify it by distributing the numbers outside the parentheses to the terms inside. We will then combine like terms and isolate the variable $x$ to one side of the equation.

Distributing the Numbers Outside the Parentheses

The first step in solving this equation is to distribute the numbers outside the parentheses to the terms inside. In this case, we have two numbers outside the parentheses: 2 and 8. We will distribute these numbers to the terms inside the parentheses.

4x + 2(2x - 3) = 8(x - 1)

Distributing the 2 to the terms inside the parentheses, we get:

4x + 4x - 6 = 8x - 8

Distributing the 8 to the terms inside the parentheses, we get:

4x + 4x - 6 = 8x - 8

Combining Like Terms

Now that we have distributed the numbers outside the parentheses to the terms inside, we can combine like terms. In this case, we have two like terms: 4x and 4x. We can combine these terms by adding them together.

8x - 6 = 8x - 8

Isolating the Variable $x$

Now that we have combined like terms, we can isolate the variable $x$ to one side of the equation. To do this, we will add 6 to both sides of the equation.

8x - 6 + 6 = 8x - 8 + 6

Simplifying the equation, we get:

8x = 8x - 2

Conclusion

Now that we have isolated the variable $x$ to one side of the equation, we can see that the equation is true for all values of $x$ . This is because the left-hand side of the equation is equal to the right-hand side of the equation for any value of $x$ .

Final Answer

The final answer is C. This equation is true for all values of $x$ .

Introduction

In this section, we will be answering some frequently asked questions about the equation $4x + 2(2x - 3) = 8(x - 1)$ . We will cover topics such as how to simplify the equation, how to combine like terms, and how to isolate the variable $x$ .

Q&A

Q: How do I simplify the equation $4x + 2(2x - 3) = 8(x - 1)$ ?

A: To simplify the equation, you need to distribute the numbers outside the parentheses to the terms inside. In this case, you have two numbers outside the parentheses: 2 and 8. You will distribute these numbers to the terms inside the parentheses.

4x + 2(2x - 3) = 8(x - 1)

Distributing the 2 to the terms inside the parentheses, you get:

4x + 4x - 6 = 8x - 8

Distributing the 8 to the terms inside the parentheses, you get:

4x + 4x - 6 = 8x - 8

Q: How do I combine like terms in the equation $4x + 4x - 6 = 8x - 8$ ?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. In this case, you have two like terms: 4x and 4x. You can combine these terms by adding them together.

8x - 6 = 8x - 8

Q: How do I isolate the variable $x$ in the equation $8x - 6 = 8x - 8$ ?

A: To isolate the variable $x$ , you need to get all the terms with $x$ on one side of the equation and all the constant terms on the other side. In this case, you can add 6 to both sides of the equation to isolate the variable $x$ .

8x - 6 + 6 = 8x - 8 + 6

Simplifying the equation, you get:

8x = 8x - 2

Q: What is the final answer to the equation $4x + 2(2x - 3) = 8(x - 1)$ ?

A: The final answer to the equation is C. This equation is true for all values of $x$ . This is because the left-hand side of the equation is equal to the right-hand side of the equation for any value of $x$ .

Conclusion

In this Q&A section, we have covered some frequently asked questions about the equation $4x + 2(2x - 3) = 8(x - 1)$ . We have discussed how to simplify the equation, how to combine like terms, and how to isolate the variable $x$ . We have also provided the final answer to the equation, which is C. This equation is true for all values of $x$ .

Final Answer

The final answer is C. This equation is true for all values of $x$ .