SAT II Math I : Single-Variable Algebra

Example Questions

Example Question #1 : Solving Equations

Solve for in terms of :

Explanation:

To solve this equation in terms of y, we must isolate it. We start by moving those terms, that do not involve y, to the right hand side. Thus, we add 6 to both sides.

Next, since there are no other terms on the left hand side that do not include y, we must factor a y out of them.

Now, we can divide to isolate y.

Example Question #2 : Solving Equations

Solve for the unknown variable:

Explanation:

To solve , group like terms on one side of the equal sign.

Example Question #3 : Solving Equations

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.

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

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

Example Question #4 : Solving Equations

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.

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

Example Question #2 : Solving Equations

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.

Subtract  on both sides.

Multiply  on both sides.

Example Question #1 : Solving Equations

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.

Multiply  on both sides. When multiplying with another negative number, our answer is positive.

Example Question #6 : Solving Equations

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.

Divide  on both sides.

Example Question #7 : Solving Equations

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.

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

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

Example Question #11 : 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.

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

Multiply  on both sides.

Example Question #12 : 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.

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

When multiplying with another negative number, our answer is positive.