SAT II Math I : Solving Equations

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

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Example Question #1 : Solving Equations

Solve for .

 

Possible Answers:

Correct answer:

Explanation:

Add 9 to each side of the equation.

Multiply each side of the equation by 4.

Example Question #2 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

To isolate , we must first eliminate the fraction on the left hand side by multiplying each side by 3.

Next, 5 must be subtracted fromm both sides.

Finally, 2 must be divided out of each side.

Thus, this is our answer.

 

Example Question #3 : Solving Equations

Solve for in terms of :

Possible Answers:

Correct answer:

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 #4 : Solving Equations

Solve for the unknown variable:  

Possible Answers:

Correct answer:

Explanation:

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

Example Question #5 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

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 #6 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

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. When adding with another negative number, just treat as an addition problem and then add a negative sign in front.

 

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

Example Question #7 : Solving Equations

Possible Answers:

Correct answer:

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 #8 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

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. When adding with another negative number, just treat as an addition problem and then add a negative sign in front.

 

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

Example Question #9 : Solving Equations

Solve for .

Possible Answers:

Correct answer:

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.

 

Divide  on both sides.

Example Question #10 : Solving Equations

Possible Answers:

Correct answer:

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.

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