Match the operation with its inverse operation you would use to solve an equation for a variable. (7 points) \( \square \) Addition \( \square \) Multiplication \( \square \) Subtraction Division \( \sqrt{x} \) \( x^{2} \) \( \sqrt[3]{x} \) Addition : \( : \sqrt{x} \) Division Multiplication Subtraction : \( x^{3} \) : \( x^{2} \)

To match each operation with its corresponding inverse operation, we can analyze each operation and determine what operation would reverse its effect. Here’s the breakdown: 1. **Addition**: The inverse operation is **Subtraction**. - If you add a number to a variable, you can subtract that same number to isolate the variable. 2. **Multiplication**: The inverse operation is **Division**. - If you multiply a variable by a number, you can divide by that same number to isolate the variable. 3. **Subtraction**: The inverse operation is **Addition**. - If you subtract a number from a variable, you can add that same number back to isolate the variable. 4. **Square Root**: The inverse operation is **Squaring** (or raising to the power of 2). - If you take the square root of a variable, squaring it will return to the original value. 5. **Cubed Root**: The inverse operation is **Cubing** (or raising to the power of 3). - If you take the cube root of a variable, cubing it will return to the original value. Now, let's match them: - **Addition**: \( \square \) **Subtraction** - **Multiplication**: \( \square \) **Division** - **Subtraction**: \( \square \) **Addition** - **Square Root**: \( \sqrt{x} \) \( \square \) **Squaring** \( (x^{2}) \) - **Cubed Root**: \( \sqrt[3]{x} \) \( \square \) **Cubing** \( (x^{3}) \) So the final matches are: - Addition: **Subtraction** - Multiplication: **Division** - Subtraction: **Addition** - \( \sqrt{x} \): \( x^{2} \) - \( \sqrt[3]{x} \): \( x^{3} \)