Algebra 1 : How to solve absolute value equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #21 : How To Solve Absolute Value Equations

Possible Answers:

Correct answer:

Explanation:

Example Question #22 : How To Solve Absolute Value Equations

Solve for all possible values of .

Possible Answers:

Correct answer:

Explanation:

First, ignore absolute value signs and solve for x.

Now, for the other solution, ignore absolute value signs and change the sign of the right side of the equation. Solve for x.

Example Question #23 : How To Solve Absolute Value Equations

Solve for all values of .

Possible Answers:

Correct answer:

Explanation:

First, make sure to have the absolute value part of the equation by itself on the left side.

Now solve for both x values.

Change the side of the right hand side to find the other value of x.

Example Question #24 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

The question is asking for the value of . To isolate , we must first isolate the absolute value expression.

The absolute value bars give a positive value to the result of the expression within. This means the real value of the inner expression could be positive or negative. To find the two values of , create the two possible equations. 

   

Balance the equations to find .

--

--

Therefore, and

Also written as .

Example Question #25 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

 

Divide both sides by , we get .

Final answer is .

Example Question #26 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

 

Subtract both sides by , we get 

 

Distribute the negative sign to get .

Add both sides by  and divide both sides by  to get .

Final answer is .

Example Question #21 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

 

Add both sides by , we get 

 

Distribute the negative sign to get .

Subtract both sides by  and divide both sides by  to get .

Final answer is .

Example Question #28 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

 

Subtract both sides by , we get 

 

Distribute the negative sign to get .

Add both sides by  and divide both sides by  to get .

Final answer is .

Example Question #29 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers.

 

Cross multiply and we get .

 

Cross multiply and divide both sides by , we get .

Final answer is .

Example Question #30 : How To Solve Absolute Value Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving with absolute values, we need to consider both positive and negative answers. Let's first divide both sides by . We have:

 

Divide both sides by , we get .

Final answer is .

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