Solve The Two-step Equation And Identify The Steps.$1.4x + 6.1 = -7.9$1. The First Step Is To $\square$ On Both Sides.2. The Second Step Is To $\square$ On Both Sides.The Solution Is $x = $ $\square$A.

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Introduction

Two-step equations are a fundamental concept in algebra, and solving them requires a clear understanding of the steps involved. In this article, we will guide you through the process of solving a two-step equation, using the equation 1.4x+6.1=−7.91.4x + 6.1 = -7.9 as an example. We will break down the solution into two steps, and provide a clear explanation of each step.

Step 1: Isolate the Variable

The first step in solving a two-step equation is to isolate the variable. In this case, we need to get rid of the constant term on the left-hand side of the equation. To do this, we will subtract 6.16.1 from both sides of the equation.

Subtracting 6.1 from both sides

1.4x+6.1−6.1=−7.9−6.11.4x + 6.1 - 6.1 = -7.9 - 6.1

This simplifies to:

1.4x=−13.91.4x = -13.9

Explanation

When we subtract 6.16.1 from both sides of the equation, we are essentially getting rid of the constant term on the left-hand side. This leaves us with the variable term, 1.4x1.4x, on the left-hand side, and the constant term, −13.9-13.9, on the right-hand side.

Step 2: Solve for the Variable

The second step in solving a two-step equation is to solve for the variable. In this case, we need to get rid of the coefficient of the variable, 1.41.4. To do this, we will divide both sides of the equation by 1.41.4.

Dividing both sides by 1.4

1.4x1.4=−13.91.4\frac{1.4x}{1.4} = \frac{-13.9}{1.4}

This simplifies to:

x=−10x = -10

Explanation

When we divide both sides of the equation by 1.41.4, we are essentially getting rid of the coefficient of the variable. This leaves us with the variable, xx, on the left-hand side, and the constant term, −10-10, on the right-hand side.

Conclusion

In this article, we have guided you through the process of solving a two-step equation, using the equation 1.4x+6.1=−7.91.4x + 6.1 = -7.9 as an example. We have broken down the solution into two steps, and provided a clear explanation of each step. By following these steps, you should be able to solve two-step equations with ease.

Tips and Tricks

  • Make sure to follow the order of operations when solving two-step equations. This means that you should perform any calculations inside parentheses first, followed by any exponents, and then any multiplication and division, and finally any addition and subtraction.
  • When isolating the variable, make sure to get rid of any constant terms on the left-hand side of the equation.
  • When solving for the variable, make sure to get rid of any coefficients of the variable.

Common Mistakes

  • Failing to follow the order of operations when solving two-step equations.
  • Not getting rid of constant terms on the left-hand side of the equation when isolating the variable.
  • Not getting rid of coefficients of the variable when solving for the variable.

Real-World Applications

Two-step equations have many real-world applications, including:

  • Finance: When calculating interest rates or investment returns, two-step equations can be used to solve for the unknown variable.
  • Science: When measuring the rate of change of a physical quantity, two-step equations can be used to solve for the unknown variable.
  • Engineering: When designing a system or structure, two-step equations can be used to solve for the unknown variable.

Conclusion

Introduction

In our previous article, we guided you through the process of solving a two-step equation, using the equation 1.4x+6.1=−7.91.4x + 6.1 = -7.9 as an example. In this article, we will answer some common questions that students often have when solving two-step equations.

Q: What is a two-step equation?

A two-step equation is an equation that requires two steps to solve. The first step is to isolate the variable, and the second step is to solve for the variable.

Q: How do I know which operation to perform first?

When solving a two-step equation, you should follow the order of operations. This means that you should perform any calculations inside parentheses first, followed by any exponents, and then any multiplication and division, and finally any addition and subtraction.

Q: What is the difference between isolating the variable and solving for the variable?

Isolating the variable means getting rid of any constant terms on the left-hand side of the equation, so that the variable is by itself. Solving for the variable means getting rid of any coefficients of the variable, so that the variable is equal to a constant.

Q: How do I know if I need to add or subtract a value from both sides of the equation?

When solving a two-step equation, you should add or subtract a value from both sides of the equation to get rid of any constant terms on the left-hand side of the equation.

Q: What if I have a fraction as a coefficient of the variable?

If you have a fraction as a coefficient of the variable, you can multiply both sides of the equation by the reciprocal of the fraction to get rid of the fraction.

Q: Can I use a calculator to solve two-step equations?

Yes, you can use a calculator to solve two-step equations. However, it's always a good idea to check your work by plugging the solution back into the original equation.

Q: What if I get stuck on a two-step equation?

If you get stuck on a two-step equation, try breaking it down into smaller steps. You can also try using a different method, such as graphing the equation or using a calculator.

Q: Are two-step equations used in real-world applications?

Yes, two-step equations are used in many real-world applications, including finance, science, and engineering.

Q: Can I use two-step equations to solve systems of equations?

Yes, you can use two-step equations to solve systems of equations. However, you will need to use a different method, such as substitution or elimination.

Conclusion

In conclusion, solving two-step equations is a fundamental concept in algebra, and requires a clear understanding of the steps involved. By following the steps outlined in this article, you should be able to solve two-step equations with ease. Remember to follow the order of operations, isolate the variable, and solve for the variable. With practice and patience, you will become proficient in solving two-step equations and be able to apply them to real-world problems.

Common Mistakes

  • Failing to follow the order of operations when solving two-step equations.
  • Not getting rid of constant terms on the left-hand side of the equation when isolating the variable.
  • Not getting rid of coefficients of the variable when solving for the variable.

Tips and Tricks

  • Make sure to follow the order of operations when solving two-step equations.
  • When isolating the variable, make sure to get rid of any constant terms on the left-hand side of the equation.
  • When solving for the variable, make sure to get rid of any coefficients of the variable.

Real-World Applications

Two-step equations have many real-world applications, including:

  • Finance: When calculating interest rates or investment returns, two-step equations can be used to solve for the unknown variable.
  • Science: When measuring the rate of change of a physical quantity, two-step equations can be used to solve for the unknown variable.
  • Engineering: When designing a system or structure, two-step equations can be used to solve for the unknown variable.

Conclusion

In conclusion, solving two-step equations is a fundamental concept in algebra, and requires a clear understanding of the steps involved. By following the steps outlined in this article, you should be able to solve two-step equations with ease. Remember to follow the order of operations, isolate the variable, and solve for the variable. With practice and patience, you will become proficient in solving two-step equations and be able to apply them to real-world problems.