1. A variable is a letter or symbol that represents an unknown number.
2. To solve an equation, you should always add first, then multiply.
3. The equation \( 3x + 7 = 16 \) is an example of a two-step equation.
4. Subtracting 5 from both sides of an equation is an example of using an inverse operation.
5. The solution to an equation is the value of the variable that makes the equation false.
✏️ 2. Fill in the Blanks
1. An is a mathematical statement that shows two expressions are equal.
2. To undo addition, you use the inverse operation of .
3. In the equation \( 4x - 8 = 12 \), the number 8 is a .
4. When solving two-step equations, you generally perform the and subtraction operations before multiplication and division.
5. The value of the variable that makes an equation true is called the .
🔗 3. Matching
« A letter or symbol used to represent an unknown quantity.
« A mathematical statement showing that two expressions are equal.
« Operations that undo each other, such as addition and subtraction.
« A number in an equation that does not change its value.
« The value of the variable that makes an equation true.
✍️ 4. Short Answer Questions
1. What is the main goal when solving any equation?
💡 Suggested Answer: The main goal is to isolate the variable on one side of the equation to find its value.
2. Explain why inverse operations are important when solving two-step equations.
💡 Suggested Answer: Inverse operations are important because they allow us to undo the operations performed on the variable, helping us to isolate it and find its value. For example, subtraction undoes addition.
🎯 5. Multiple Choice
1. Which of the following is a two-step equation?
2. Solve for \( x \): \( 2x + 3 = 13 \)
3. If \( 4x - 6 = 18 \), what is the value of \( x \)?
📝 6. Open-Ended Questions
1. Solve the equation \( 5x + 10 = 35 \). Show your steps.
💡 Solution Steps:
To solve \( 5x + 10 = 35 \):
Step 1: Subtract 10 from both sides of the equation to isolate the term with the variable.
\( 5x + 10 - 10 = 35 - 10 \)
\( 5x = 25 \)
Step 2: Divide both sides by 5 to solve for \( x \).
\( \frac{5x}{5} = \frac{25}{5} \)
\( x = 5 \)
The solution is \( x = 5 \).
2. Find the value of \( y \) in the equation \( \frac{y}{3} - 4 = 2 \). Show your steps.
💡 Solution Steps:
To solve \( \frac{y}{3} - 4 = 2 \):
Step 1: Add 4 to both sides of the equation to isolate the term with the variable.
\( \frac{y}{3} - 4 + 4 = 2 + 4 \)
\( \frac{y}{3} = 6 \)
Step 2: Multiply both sides by 3 to solve for \( y \).
\( \frac{y}{3} \times 3 = 6 \times 3 \)
\( y = 18 \)
The solution is \( y = 18 \).
3. Solve the equation \( 7 + 2p = 19 \). Show your steps.
💡 Solution Steps:
To solve \( 7 + 2p = 19 \):
Step 1: Subtract 7 from both sides of the equation to isolate the term with the variable.
\( 7 + 2p - 7 = 19 - 7 \)
\( 2p = 12 \)
Step 2: Divide both sides by 2 to solve for \( p \).
\( \frac{2p}{2} = \frac{12}{2} \)
\( p = 6 \)
The solution is \( p = 6 \).
Name Surname: .................................. Date: .... / .... / 202...
Two-Step Equations Worksheet
SCORE
A. True (T) / False (F)
( .... )
A variable is a letter or symbol that represents an unknown number.
( .... )
To solve an equation, you should always add first, then multiply.
( .... )
The equation \( 3x + 7 = 16 \) is an example of a two-step equation.
( .... )
Subtracting 5 from both sides of an equation is an example of using an inverse operation.
( .... )
The solution to an equation is the value of the variable that makes the equation false.
B. Fill in the Blanks
1)
An .................... is a mathematical statement that shows two expressions are equal.
2)
To undo addition, you use the inverse operation of .....................
3)
In the equation \( 4x - 8 = 12 \), the number 8 is a .....................
4)
When solving two-step equations, you generally perform the .................... and subtraction operations before multiplication and division.
5)
The value of the variable that makes an equation true is called the .....................
C. Matching Concepts
( .... )
A letter or symbol used to represent an unknown quantity.
- Equation
( .... )
A mathematical statement showing that two expressions are equal.
- Constant
( .... )
Operations that undo each other, such as addition and subtraction.
- Inverse Operations
( .... )
A number in an equation that does not change its value.
- Variable
( .... )
The value of the variable that makes an equation true.
- Solution
D. Short Answer Questions
1)
What is the main goal when solving any equation?
2)
Explain why inverse operations are important when solving two-step equations.
E. Multiple Choice Questions
1)
Which of the following is a two-step equation?
A) \( x + 5 = 12 \)B) \( 2x = 10 \)C) \( 3x - 4 = 11 \)D) \( x = 7 \)
2)
Solve for \( x \): \( 2x + 3 = 13 \)
A) \( x = 3 \)B) \( x = 5 \)C) \( x = 8 \)D) \( x = 10 \)
3)
If \( 4x - 6 = 18 \), what is the value of \( x \)?
A) \( x = 3 \)B) \( x = 4 \)C) \( x = 6 \)D) \( x = 8 \)
F. Open-Ended Questions
1)
Solve the equation \( 5x + 10 = 35 \). Show your steps.
2)
Find the value of \( y \) in the equation \( \frac{y}{3} - 4 = 2 \). Show your steps.
3)
Solve the equation \( 7 + 2p = 19 \). Show your steps.