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 : $$ x^{3} $$ : $$ x^{2} $$

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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**
- $$ \sqrt{x} $$: $$ x^{2} $$
- $$ \sqrt[3]{x} $$: $$ x^{3} $$
- Addition: Subtraction - Multiplication: Division - Subtraction: Addition - Square Root: Squaring ($$ x^{2} $$) - Cubed Root: Cubing ($$ x^{3} $$)

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