# SAT II Math I : Single-Variable Algebra

## Example Questions

### Example Question #21 : Single Variable Algebra

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

To get rid of the radical, we square both sides.

### Example Question #21 : Single Variable Algebra

Solve for .

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

To get rid of the radical, we square both sides.

Subtract  on both sides.

### Example Question #22 : Single Variable Algebra

Solve for .

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

Take the square root on both sides.  Remember when you do that, you need to take account of the negative as well. Two negatives multipied is a positive number.

### Example Question #23 : Single Variable Algebra

Solve for .

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

This is a quadratic equation. We need to find two terms that are factors of the c term that add up to the b term.

In this case, we should have

Solve each binomial individually.

Subtract  on both sides.

Subtract  on both sides.

### Example Question #25 : Single Variable Algebra

Solve for .

Explanation:

Subtract  on both sides.

### Example Question #24 : Single Variable Algebra

Solve for .

Explanation:

Subtract  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a normal subtraction.

Solve for .

Explanation:

### Example Question #25 : Single Variable Algebra

Solve for .

Explanation:

Add  on both sides. Since  is greater than  and is negative, our answer is negative. We treat as a normal subtraction.

### Example Question #26 : Single Variable Algebra

Solve for .

Explanation:

Divide  on both sides. When dividing with a positive number, our answer is negative.

Solve for .