Fill In The Empty Slots By Dragging Tiles From The Left To Show The Next Step For Solving The Equation.Solve The Two-step Equation: $\frac{3}{4}(x) - 1.72 = -6.82$1. The First Step Is To ____ On Both Sides.2. The Second Step Is To ____ On Both

Introduction

Two-step equations are a fundamental concept in algebra that require students to solve a linear equation in two steps. These equations involve a variable (x) and a constant, and the goal is to isolate the variable on one side of the equation. In this article, we will guide you through the process of solving a two-step equation using a step-by-step approach.

Understanding the Problem

The given equation is $\frac{3}{4}(x) - 1.72 = -6.82$. To solve this equation, we need to isolate the variable x on one side of the equation. The equation involves a fraction, a constant, and a variable, making it a two-step equation.

Step 1: Add 1.72 to Both Sides

The first step in solving the equation is to add 1.72 to both sides of the equation. This will eliminate the constant term on the left side of the equation.

$\frac{3}{4}(x) - 1.72 + 1.72 = -6.82 + 1.72$

Simplifying the equation, we get:

$\frac{3}{4}(x) = -5.10$

**Step 2: Multiply Both Sides by $\frac{4}{3}$

The second step in solving the equation is to multiply both sides of the equation by $\frac{4}{3}$. This will eliminate the fraction on the left side of the equation.

$\frac{3}{4}(x) \times \frac{4}{3} = -5.10 \times \frac{4}{3}$

Simplifying the equation, we get:

$x = -6.80$

Conclusion

In this article, we have solved a two-step equation using a step-by-step approach. We added 1.72 to both sides of the equation to eliminate the constant term, and then multiplied both sides by $\frac{4}{3}$ to eliminate the fraction. The final solution is x = -6.80.

Tips and Tricks

• When solving two-step equations, it's essential to follow the order of operations (PEMDAS).
• Make sure to simplify the equation at each step to avoid errors.
• Use a calculator to check your solution and ensure that it's accurate.

Practice Problems

Try solving the following two-step equations:

1. $\frac{2}{3}(x) + 2.50 = 5.50$
2. $\frac{5}{6}(x) - 3.20 = 2.40$

Discussion

What are some common mistakes students make when solving two-step equations? How can we avoid these mistakes and improve our problem-solving skills?

References

• [Algebra textbook]
• [Online math resources]

Related Articles

• Solving Linear Equations
• Solving Quadratic Equations
• Introduction to Algebra

Introduction

In our previous article, we provided a step-by-step guide on solving two-step equations. However, we understand that sometimes, it's not enough to just follow a guide. You may have questions, doubts, or need further clarification on certain concepts. That's why we've put together this Q&A article to address some of the most common questions and concerns related to solving two-step equations.

Q: What is a two-step equation?

A two-step equation is a linear equation that requires two steps to solve. It involves a variable (x) and a constant, and the goal is to isolate the variable on one side of the equation.

Q: What are the two steps involved in solving a two-step equation?

The two steps involved in solving a two-step equation are:

1. Adding or subtracting a constant to both sides of the equation to eliminate the constant term.
2. Multiplying or dividing both sides of the equation by a coefficient to eliminate the fraction.

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

When solving a two-step equation, it's essential to follow the order of operations (PEMDAS). This means that you should perform the operations in the following order:

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

Q: What if I have a fraction on both sides of the equation?

If you have a fraction on both sides of the equation, you can eliminate the fraction by multiplying both sides of the equation by the reciprocal of the fraction. For example, if you have $\frac{1}{2}(x) = 3$, you can multiply both sides by 2 to get $x = 6$.

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 essential to check your solution to ensure that it's accurate. You can do this by plugging your solution back into the original equation and verifying that it's true.

Q: What are some common mistakes to avoid when solving two-step equations?

Some common mistakes to avoid when solving two-step equations include:

• Not following the order of operations (PEMDAS)
• Not simplifying the equation at each step
• Not checking your solution to ensure that it's accurate

Q: How can I practice solving two-step equations?

You can practice solving two-step equations by working through a series of problems. You can find practice problems in your algebra textbook or online. You can also try solving problems on your own or with a partner.

Q: What are some real-world applications of two-step equations?

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

• Finance: Calculating interest rates and investments
• Science: Measuring the rate of change of a quantity
• Engineering: Designing and building structures

Conclusion

Solving two-step equations can be challenging, but with practice and patience, you can master this skill. Remember to follow the order of operations (PEMDAS), simplify the equation at each step, and check your solution to ensure that it's accurate. With these tips and tricks, you'll be solving two-step equations like a pro in no time!

Practice Problems

Try solving the following two-step equations:

1. $\frac{2}{3}(x) + 2.50 = 5.50$
2. $\frac{5}{6}(x) - 3.20 = 2.40$

Discussion

What are some common mistakes you've made when solving two-step equations? How have you overcome these mistakes? Share your experiences and tips with us!

References

• [Algebra textbook]
• [Online math resources]

Related Articles

• Solving Linear Equations
• Solving Quadratic Equations
• Introduction to Algebra