Solve The Equation:${ 5 - 2(3 - X) = 4x + 10 }$

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Introduction

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In this article, we will delve into the world of algebra and solve a linear equation step by step. The equation we will be solving is: $5 - 2(3 - x) = 4x + 10$. This equation may seem daunting at first, but with a clear understanding of the order of operations and some basic algebraic manipulations, we can easily solve for the variable $x$.

Understanding the Equation

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Before we begin solving the equation, let's take a closer look at what we're dealing with. The equation is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, our equation is $5 - 2(3 - x) = 4x + 10$. Our goal is to isolate the variable $x$ and find its value.

Distributing the Negative Sign

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The first step in solving this equation is to distribute the negative sign inside the parentheses. This means we need to multiply the negative sign by each term inside the parentheses. So, $-2(3 - x)$ becomes $-6 + 2x$. Now our equation looks like this: $5 - 6 + 2x = 4x + 10$.

Simplifying the Equation

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Next, we need to simplify the equation by combining like terms. On the left-hand side of the equation, we have $5 - 6$, which simplifies to $-1$. So, our equation now looks like this: $-1 + 2x = 4x + 10$.

Isolating the Variable

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Now that we have simplified the equation, we can start isolating the variable $x$. To do this, we need to get all the terms with $x$ on one side of the equation. We can do this by subtracting $2x$ from both sides of the equation. This gives us: $-1 = 2x + 4x + 10$.

Combining Like Terms

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Next, we need to combine like terms on the right-hand side of the equation. We have $2x + 4x$, which simplifies to $6x$. So, our equation now looks like this: $-1 = 6x + 10$.

Subtracting 10 from Both Sides

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Now that we have combined like terms, we can start isolating the variable $x$ further. To do this, we need to get rid of the constant term on the right-hand side of the equation. We can do this by subtracting $10$ from both sides of the equation. This gives us: $-1 - 10 = 6x$.

Simplifying the Equation

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Next, we need to simplify the equation by combining like terms. On the left-hand side of the equation, we have $-1 - 10$, which simplifies to $-11$. So, our equation now looks like this: $-11 = 6x$.

Dividing Both Sides by 6

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Finally, we can solve for the variable $x$ by dividing both sides of the equation by $6$. This gives us: $x = -11/6$.

Conclusion

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And there you have it! We have successfully solved the equation $5 - 2(3 - x) = 4x + 10$. By following the order of operations and using basic algebraic manipulations, we were able to isolate the variable $x$ and find its value. This equation may have seemed daunting at first, but with a clear understanding of the steps involved, we can easily solve it.

Frequently Asked Questions

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Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I simplify an equation?

A: To simplify an equation, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. We can combine like terms by adding or subtracting their coefficients.

Q: How do I isolate a variable?

A: To isolate a variable, we need to get all the terms with the variable on one side of the equation. We can do this by adding or subtracting the same value to both sides of the equation.

Final Answer

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The final answer is: $\boxed{-11/6}$

=====================================================

Introduction

---

In this article, we will delve into the world of algebra and solve a linear equation step by step. The equation we will be solving is: $5 - 2(3 - x) = 4x + 10$. This equation may seem daunting at first, but with a clear understanding of the order of operations and some basic algebraic manipulations, we can easily solve for the variable $x$.

Understanding the Equation

---

Before we begin solving the equation, let's take a closer look at what we're dealing with. The equation is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, our equation is $5 - 2(3 - x) = 4x + 10$. Our goal is to isolate the variable $x$ and find its value.

Distributing the Negative Sign

---

The first step in solving this equation is to distribute the negative sign inside the parentheses. This means we need to multiply the negative sign by each term inside the parentheses. So, $-2(3 - x)$ becomes $-6 + 2x$. Now our equation looks like this: $5 - 6 + 2x = 4x + 10$.

Simplifying the Equation

---

Next, we need to simplify the equation by combining like terms. On the left-hand side of the equation, we have $5 - 6$, which simplifies to $-1$. So, our equation now looks like this: $-1 + 2x = 4x + 10$.

Isolating the Variable

---

Now that we have simplified the equation, we can start isolating the variable $x$. To do this, we need to get all the terms with $x$ on one side of the equation. We can do this by subtracting $2x$ from both sides of the equation. This gives us: $-1 = 2x + 4x + 10$.

Combining Like Terms

---

Next, we need to combine like terms on the right-hand side of the equation. We have $2x + 4x$, which simplifies to $6x$. So, our equation now looks like this: $-1 = 6x + 10$.

Subtracting 10 from Both Sides

---

Now that we have combined like terms, we can start isolating the variable $x$ further. To do this, we need to get rid of the constant term on the right-hand side of the equation. We can do this by subtracting $10$ from both sides of the equation. This gives us: $-1 - 10 = 6x$.

Simplifying the Equation

---

Next, we need to simplify the equation by combining like terms. On the left-hand side of the equation, we have $-1 - 10$, which simplifies to $-11$. So, our equation now looks like this: $-11 = 6x$.

Dividing Both Sides by 6

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Finally, we can solve for the variable $x$ by dividing both sides of the equation by $6$. This gives us: $x = -11/6$.

Conclusion

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And there you have it! We have successfully solved the equation $5 - 2(3 - x) = 4x + 10$. By following the order of operations and using basic algebraic manipulations, we were able to isolate the variable $x$ and find its value. This equation may have seemed daunting at first, but with a clear understanding of the steps involved, we can easily solve it.

Frequently Asked Questions

---

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I simplify an equation?

A: To simplify an equation, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. We can combine like terms by adding or subtracting their coefficients.

Q: How do I isolate a variable?

A: To isolate a variable, we need to get all the terms with the variable on one side of the equation. We can do this by adding or subtracting the same value to both sides of the equation.

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 is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, we can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. We can also use factoring or the quadratic formula to solve a quadratic equation.

Q: What is the difference between a system of linear equations and a system of quadratic equations?

A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. A system of quadratic equations is a set of two or more quadratic equations that are solved simultaneously.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, we can use substitution or elimination. We can also use matrices to solve a system of linear equations.

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

A: A linear inequality is an inequality in which the highest power of the variable is 1. A quadratic inequality is an inequality in which the highest power of the variable is 2.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, we can use the following steps: 1) isolate the variable, 2) determine the direction of the inequality, and 3) graph the solution.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, we can use the following steps: 1) factor the quadratic expression, 2) determine the direction of the inequality, and 3) graph the solution.

Final Answer

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The final answer is: $\boxed{-11/6}$