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

TLDRThis educational video teaches how to solve two-step equations, a fundamental algebra skill for Grade 7. The presenter demonstrates solving the equation 7x + 3 = 38 by first isolating the term with the variable, then using inverse operations to isolate x. The process involves subtracting 3 from both sides to eliminate the constant, and then dividing by 7 to solve for x. The solution, x = 5, is verified by substituting back into the original equation. The video emphasizes the importance of checking work to ensure accuracy.

### Takeaways

- π Solving two-step equations involves manipulating the equation in two steps to isolate the variable.
- π’ The first step often involves eliminating the constant term attached to the variable by using its inverse operation.
- β In the example, subtracting 3 from both sides of the equation (7x + 3 = 38) helps to isolate the term with the variable.
- β After the first step, the equation becomes (7x = 35), moving closer to isolating the variable x.
- π The second step involves dealing with the coefficient of the variable, using division as the inverse operation of multiplication.
- π Dividing both sides of the equation (7x = 35) by 7 results in (x = 5), finding the value of x.
- π To verify the solution, substitute the found value of x back into the original equation to check if both sides balance.
- π The check involves performing the same operations on both sides of the equation to ensure the solution is correct.
- π― The final solution is confirmed when the substituted value of x makes both sides of the equation equal, proving the solution is accurate.
- π It's crucial to remember to perform the same operation on both sides of the equation to maintain equality.
- π The process highlights the importance of checking work to ensure the accuracy of the solution in algebraic equations.

### 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 start solving a two-step equation?

-You start by manipulating the equation to get the variable, typically 'x', by itself.

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

-The first step is to isolate the term with the variable by performing the inverse operation of the number attached to the variable. In this case, subtracting 3 from both sides to eliminate the +3.

### What is the inverse operation of addition?

-The inverse operation of addition is subtraction.

### After moving the +3 to the other side of the equation, what is the new equation?

-After subtracting 3 from both sides, the new equation is 7x = 35.

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

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

### What is the result of dividing both sides of the equation 7x = 35 by 7?

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

### How do you check if your solution to the equation is correct?

-You check the solution by substituting the value of 'x' back into the original equation and verifying that both sides of the equation balance.

### What is the final solution to the equation 7x + 3 = 38?

-The final solution is x = 5.

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

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

### What is the general approach for solving two-step equations?

-The general approach is to manipulate the equation to isolate the variable, solve for the variable, and then check the solution by substituting it back into the original equation.

### Outlines

### π Solving Two-Step Equations

This video segment teaches viewers how to solve two-step equations, which are algebraic equations that require two steps to isolate the variable. The example given is 7x + 3 = 38. The process involves manipulating the equation to isolate 'x' by performing inverse operations. In this case, subtracting 3 from both sides to eliminate the constant on the left side, resulting in 7x = 35. Then, dividing both sides by 7 to solve for 'x', yielding x = 5. The video 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

### π‘Two-Step Equations

### π‘Manipulate

### π‘Inverse Operation

### π‘Isolate the Variable

### π‘Coefficient

### π‘Division

### π‘Check Your Work

### π‘Balanced Equation

### π‘Variable

### π‘Equation

### π‘Solution

### Highlights

Introduction to solving two-step equations in algebra.

A two-step equation requires two operations to isolate the variable.

The first example presented is 7x + 3 = 38.

The goal is to manipulate the equation to isolate x.

To remove the constant term, perform the inverse operation on both sides.

Subtract 3 from both sides to eliminate the constant term.

After subtraction, the equation becomes 7x = 35.

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

Division leads to x = 5 as the solution.

Checking the solution involves substituting the value of x back into the original equation.

Verification shows that 7(5) + 3 equals the original right-hand side, 38.

The importance of checking work to ensure the solution is correct.

The process of solving two-step equations involves two main steps: manipulation and verification.

The final solution is x = 5, confirmed by checking.

A summary of the steps to solve two-step equations.

The significance of using inverse operations to isolate the variable.

The method of checking the solution by substituting back into the original equation.

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