Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

Example Question #25 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides.

 Divide  on both sides.

Example Question #26 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides.

 Divide  on both sides. When dividing with a negative number, our answer is negative. Also, we must FLIP the inequality.

Example Question #28 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Subtract  on both sides. When adding with another negative number, we just add the numbers and put a minus sign in front.

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

Example Question #27 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Multiply  on both sides.

Example Question #28 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Divide  on both sides. When dividing with another negative number, our answer is positive. We also need to FLIP the inequality sign.

Example Question #31 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Multiply  on both sides. Remember to FLIP the inequality.

Example Question #32 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Add  on both sides.

 Multiply  on both sides. Remember to FLIP the inequality sign. If you try to multiply both sides by , you will have the wrong answer. When dealing with inequality equations, always multiply or divide the positive number in front of the variable.

Example Question #33 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

 Distribute. If you decide to divide both sides by , you will change the answer. When dealing with inequalities, distribute first. 

 Add  on both sides.

 Divide  on both sides. Remember to FLIP the inequality sign.

Example Question #34 : Solving Inequalities

Solve for .

Possible Answers:

 or 

 or 

Correct answer:

Explanation:

 Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

 Now, we need to know how to make the range for . We know if  is , this will satisfy the inequality since  is less than . Also,  is between . Our final answer is .

Example Question #32 : Solving Inequalities

Possible Answers:

 or 

 or 

Correct answer:

 or 

Explanation:

 Anytime you exponents in inequalities, you need to think of ranges of values that are acceptable. Remember, when an exponent is squared, negative values are also acceptable since two negatives multiplied are positive. We take the square root of both sides.

 Now, we need to know how to make the range for . We know if  is , this will satisfy the inequality since  is greater than . So then we know  and . Our final answer is  or .

Learning Tools by Varsity Tutors