# Solving Two-Step Equations | Expressions & Equations | Grade 7

TLDRThis educational video teaches viewers how to solve two-step equations, a fundamental algebra skill. The presenter uses the example 7x + 3 = 38, demonstrating how to isolate the variable 'x' by performing inverse operations. First, subtracting 3 from both sides to eliminate the constant term, then dividing by 7 to solve for 'x'. The solution, x = 5, is verified by substituting it back into the original equation. The video emphasizes the importance of checking work to ensure accuracy, providing a clear and concise guide for Grade 7 students learning expressions and equations.

### Takeaways

- 🔢 Solving two-step equations involves manipulating the equation to isolate the variable.
- 📘 The first step often involves dealing with constants or coefficients attached to the variable.
- ➕ To remove a constant from the left side, apply its inverse operation (subtraction) to both sides of the equation.
- 🔄 After the first step, check the equation to ensure the variable is still correctly represented.
- 📉 If the variable is multiplied by a number, use division as the inverse operation to isolate it.
- 🧐 Always perform the same operation on both sides of the equation to maintain equality.
- 🔍 After finding the solution, it's crucial to check the work by substituting the variable's value back into the original equation.
- 📊 The verification process confirms if the solution satisfies the original equation by ensuring both sides are equal.
- 📐 The goal is to simplify the equation to the point where the variable is by itself, indicating the correct solution.
- 🎓 Understanding the inverse operations (additive inverse for constants, multiplicative inverse for coefficients) is key to solving two-step equations.
- 📝 The process emphasizes the importance of both solving and verifying the solution to ensure accuracy.

### Q & A

### What is a two-step equation?

-A two-step equation is an algebra equation that requires two steps to find the final solution.

### How do you approach solving a two-step equation?

-To solve a two-step equation, you manipulate the equation to isolate the variable by itself on one side of the equation.

### What is the first step in solving the equation 7x + 3 = 38?

-The first step is to eliminate the constant term attached to the variable by performing the inverse operation, which in this case is subtracting 3 from both sides.

### What is the inverse operation of adding 3?

-The inverse operation of adding 3 is subtracting 3.

### After the first step, what is the simplified form of the equation 7x + 3 = 38?

-After subtracting 3 from both sides, the simplified form is 7x = 35.

### How do you isolate x in the equation 7x = 35?

-To isolate x, you divide both sides of the equation by 7, which is the coefficient of x.

### What is the solution to the equation 7x = 35 after performing the second step?

-After dividing both sides by 7, the solution is x = 5.

### How can you check if your solution to a two-step equation is correct?

-You can check your solution by substituting the value of x back into the original equation and verifying that both sides are equal.

### What is the final answer to the equation 7x + 3 = 38 after checking your work?

-The final answer is x = 5, which is verified by substituting it back into the equation and confirming that 7(5) + 3 equals 38.

### Why is it important to check your work when solving equations?

-Checking your work ensures that the solution is correct and helps identify any mistakes made during the solving process.

### What is the general process for solving two-step equations as described in the script?

-The general process involves manipulating the equation to isolate the variable, finding the solution, and then checking the work to confirm the solution is correct.

### Outlines

### 📘 Solving Two-Step Equations

This paragraph introduces the concept of two-step equations in algebra, which are equations that require two operations to isolate the variable. The example given is 7x + 3 = 38. The process involves first subtracting 3 from both sides to get 7x = 35, and then dividing both sides by 7 to isolate x, resulting in x = 5. The paragraph emphasizes the importance of checking the solution by substituting the value of x back into the original equation to ensure both sides balance, confirming x = 5 as the correct solution.

### Mindmap

### Keywords

### 💡Two-Step Equations

### 💡Manipulate the Equation

### 💡Inverse Operation

### 💡Isolate the Variable

### 💡Check Your Work

### 💡Variable

### 💡Coefficient

### 💡Constant

### 💡Division

### 💡Subtraction

### 💡Balanced Equation

### Highlights

Introduction to solving two-step equations in algebra.

Two-step equations require two operations to isolate the variable.

First example equation: 7x + 3 = 38.

Goal is to manipulate the equation to get x by itself.

Use inverse operations to move terms attached to x to the other side.

Subtract 3 from both sides to eliminate the constant term.

Resulting equation after subtraction: 7x = 35.

Divide both sides by 7 to solve for x.

Final solution: x = 5.

Checking work by substituting the solution back into the original equation.

Verification step: 7(5) + 3 = 38.

Confirming the solution by showing both sides of the equation are equal.

Emphasis on the importance of checking work for accuracy.

Summary of the process: manipulate the equation, solve for x, and check the work.

Reinforcement of the method for solving two-step equations.

Encouragement to practice to master the technique.