# SAT II Math I : Single-Variable Algebra

## Example Questions

### Example Question #33 : Solving Equations

Solve for .

Explanation:

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

### Example Question #34 : Solving Equations

Solve for .

Explanation:

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

### Example Question #35 : Solving Equations

Solve for .

Explanation:

Multiply both sides by . When multiplying with a positive number, our answer is negative.

### Example Question #36 : Solving Equations

Solve for .

Explanation:

Multiply both sides by . When multiplying with a negative number, our answer is negative.

Divide both sides by . When dividing with another negative number, our answer is positive.

### Example Question #37 : Solving Equations

Solve for .

Explanation:

Square both sides to get rid of the radical.

Subtract  on both sides.

### Example Question #38 : Solving Equations

Solve for .

Explanation:

Square both sides to get rid of the radical.

Multiply  on both sides.

### Example Question #47 : Single Variable Algebra

Solve for .

Explanation:

We take the square root on both sides. We also need to consider the negative answer since two negatives multiplied together is positive.

### Example Question #39 : Solving Equations

Solve for .

Explanation:

This is a quadratic equation. We can solve by factoring. We need to find teo terms that add to the b term but also multiply to get the c term.

Solve individually.

### Example Question #41 : Solving Equations

Solve for .

Explanation:

Take the square root on both sides. Remember to account for a negative square root.

We will treat as two different equations.

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

### Example Question #49 : Single Variable Algebra

Solve for .

Explanation:

Let's subtract  on both sides. It will be easier to square both sides to get rid of the radical.

This is recognition of a quadratic equation.

We need to find two terms that multiply to the c term but add up to the b term.

Solve individually for zero.