Worksheet: Solving Equations with Variables on Both Sides

📚 Topic Summary

When solving equations with variables on both sides, the key is to isolate the variable on one side of the equation. This usually involves using inverse operations to move terms around. First, simplify each side of the equation by combining like terms. Then, add or subtract terms to get all the variable terms on one side and all the constant terms on the other. Finally, multiply or divide to solve for the variable.

For example, in the equation $3x + 5 = x - 1$, we'd subtract $x$ from both sides to get $2x + 5 = -1$. Then, subtract $5$ from both sides to get $2x = -6$. Finally, divide by $2$ to find $x = -3$.

🧠 Part A: Vocabulary

Match each term with its correct definition:

1. Term
2. Variable
3. Coefficient
4. Constant
5. Inverse Operation

1. A symbol representing an unknown value.
2. A number that multiplies a variable.
3. A single number or a variable multiplied by a number.
4. A mathematical process that undoes another operation.
5. A fixed value that does not change.

(Match each number to a letter.)

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

To solve an equation with variables on both sides, we first ________ each side by combining like terms. Then, we use ________ operations to move the ________ terms to one side and the ________ terms to the other side. Finally, we ________ to isolate the variable.

🤔 Part C: Critical Thinking

Explain in your own words why it's important to perform the same operation on both sides of an equation. What happens if you don't?