When Solving The Equation, Which Is The Best First Step To Begin Simplifying The Equation?Given: \[$-2(x+3) = -10\$\]A. Multiply Both Sides By \[$-2\$\]: \[$(-2)(-2)(x+3) = -10(-2)\$\]B. Multiply Both Sides By

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When Solving the Equation, Which is the Best First Step to Begin Simplifying the Equation?

Understanding the Basics of Algebraic Equations

Algebraic equations are a fundamental concept in mathematics, and solving them requires a step-by-step approach. When faced with an equation, it's essential to identify the best first step to begin simplifying it. In this article, we'll explore the correct approach to solving the given equation: −2(x+3)=−10{-2(x+3) = -10}

The Importance of Following the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. When solving an equation, it's crucial to follow the order of operations to ensure accuracy and avoid errors. The order of operations is typically remembered using the acronym PEMDAS:

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

Analyzing the Given Equation

The given equation is: −2(x+3)=−10{-2(x+3) = -10}

To begin simplifying this equation, we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses. However, in this case, we have a coefficient of -2 outside the parentheses, which can be distributed to the terms inside the parentheses.

Distributing the Coefficient

When a coefficient is distributed to the terms inside the parentheses, it's essential to multiply the coefficient by each term inside the parentheses. In this case, we have:

−2(x+3)=−2x−6{-2(x+3) = -2x - 6}

Now, the equation becomes: −2x−6=−10{-2x - 6 = -10}

The Best First Step to Begin Simplifying the Equation

Given the equation −2x−6=−10{-2x - 6 = -10}, the best first step to begin simplifying it is to add 6 to both sides of the equation. This will eliminate the constant term on the left side of the equation, making it easier to solve for the variable x.

Adding 6 to Both Sides

When adding 6 to both sides of the equation, we get:

−2x−6+6=−10+6{-2x - 6 + 6 = -10 + 6}

Simplifying the equation, we get:

−2x=−4{-2x = -4}

Multiplying Both Sides by -2

Now that we have the equation −2x=−4{-2x = -4}, we can multiply both sides by -2 to eliminate the coefficient of x. This will give us:

(−2)(−2x)=(−2)(−4){(-2)(-2x) = (-2)(-4)}

Simplifying the equation, we get:

4x=8{4x = 8}

Dividing Both Sides by 4

Finally, we can divide both sides of the equation by 4 to solve for x:

x=84{x = \frac{8}{4}}

Simplifying the equation, we get:

x=2{x = 2}

Conclusion

In conclusion, when solving the equation −2(x+3)=−10{-2(x+3) = -10}, the best first step to begin simplifying it is to add 6 to both sides of the equation. This will eliminate the constant term on the left side of the equation, making it easier to solve for the variable x. By following the order of operations and simplifying the equation step by step, we can arrive at the correct solution.

Common Mistakes to Avoid

When solving algebraic equations, it's essential to avoid common mistakes that can lead to incorrect solutions. Some common mistakes to avoid include:

  • Not following the order of operations
  • Not distributing coefficients to terms inside parentheses
  • Not adding or subtracting the same value to both sides of the equation
  • Not multiplying or dividing both sides of the equation by the same value

Tips for Solving Algebraic Equations

When solving algebraic equations, here are some tips to keep in mind:

  • Always follow the order of operations
  • Distribute coefficients to terms inside parentheses
  • Add or subtract the same value to both sides of the equation
  • Multiply or divide both sides of the equation by the same value
  • Check your work by plugging the solution back into the original equation

By following these tips and avoiding common mistakes, you can become proficient in solving algebraic equations and arrive at the correct solutions.
Frequently Asked Questions: Solving Algebraic Equations

Q: What is the first step to begin simplifying an algebraic equation?

A: The first step to begin simplifying an algebraic equation is to follow the order of operations. This means evaluating expressions inside parentheses first, then exponents, followed by multiplication and division, and finally addition and subtraction.

Q: How do I distribute a coefficient to terms inside parentheses?

A: To distribute a coefficient to terms inside parentheses, you multiply the coefficient by each term inside the parentheses. For example, if you have the equation −2(x+3)=−10{-2(x+3) = -10}, you would multiply the coefficient -2 by each term inside the parentheses, resulting in −2x−6=−10{-2x - 6 = -10}.

Q: What is the difference between adding and subtracting the same value to both sides of an equation?

A: Adding the same value to both sides of an equation is equivalent to subtracting the same value from both sides of the equation. For example, if you have the equation x+3=5{x + 3 = 5}, adding 3 to both sides of the equation is equivalent to subtracting 3 from both sides of the equation, resulting in x=2{x = 2}.

Q: Why is it important to check my work by plugging the solution back into the original equation?

A: Checking your work by plugging the solution back into the original equation is important to ensure that the solution is correct. If the solution is not correct, it may indicate that there is an error in the solution process.

Q: What are some common mistakes to avoid when solving algebraic equations?

A: Some common mistakes to avoid when solving algebraic equations include:

  • Not following the order of operations
  • Not distributing coefficients to terms inside parentheses
  • Not adding or subtracting the same value to both sides of the equation
  • Not multiplying or dividing both sides of the equation by the same value

Q: How do I know if I have solved an algebraic equation correctly?

A: You can check if you have solved an algebraic equation correctly by plugging the solution back into the original equation. If the solution satisfies the original equation, then you have solved the equation correctly.

Q: What are some tips for solving algebraic equations?

A: Some tips for solving algebraic equations include:

  • Always follow the order of operations
  • Distribute coefficients to terms inside parentheses
  • Add or subtract the same value to both sides of the equation
  • Multiply or divide both sides of the equation by the same value
  • Check your work by plugging the solution back into the original equation

Q: Can I use a calculator to solve algebraic equations?

A: Yes, you can use a calculator to solve algebraic equations. However, it's always a good idea to check your work by plugging the solution back into the original equation to ensure that the solution is correct.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you can combine like terms, eliminate any unnecessary parentheses, and simplify any exponential expressions.

Q: What is the difference between an algebraic equation and an algebraic expression?

A: An algebraic equation is a statement that two expressions are equal, while an algebraic expression is a mathematical expression that contains variables and constants.

Q: Can I use algebraic equations to solve real-world problems?

A: Yes, algebraic equations can be used to solve real-world problems. Algebraic equations can be used to model real-world situations, such as the motion of objects, the growth of populations, and the behavior of electrical circuits.

Q: How do I know if an algebraic equation has a solution?

A: You can determine if an algebraic equation has a solution by checking if the equation is consistent. If the equation is consistent, then it has a solution. If the equation is inconsistent, then it does not have a solution.

Q: What are some common types of algebraic equations?

A: Some common types of algebraic equations include:

  • Linear equations
  • Quadratic equations
  • Polynomial equations
  • Rational equations
  • Radical equations

Q: How do I solve a linear equation?

A: To solve a linear equation, you can add or subtract the same value to both sides of the equation, or multiply or divide both sides of the equation by the same value.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula, which is x=−b±b2−4ac2a{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}.