All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
SAT Exam  >  SAT Questions  >  The equation |x + 2| = -2 has:a)Unique soluti... Start Learning for Free
The equation |x + 2| = -2 has:
  • a)
    Unique solution.
  • b)
    Two solutions.
  • c)
    Many solutions.
  • d)
    No solution.
Correct answer is option 'D'. Can you explain this answer?
Clear all your SAT doubts with EduRev
Most Upvoted Answer
The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many...
Summary:
The equation |x + 2| = -2 has no solution because the absolute value of a number is always non-negative, meaning it is always greater than or equal to zero. Therefore, it is impossible for the absolute value of a number to equal a negative value.

Explanation:
The equation |x + 2| = -2 involves the absolute value of a quantity x + 2 and sets it equal to -2. To determine the number of solutions, we need to understand the properties of absolute value.

Definition of Absolute Value:
The absolute value of a real number is its distance from zero on the number line. It is always non-negative, meaning it is always greater than or equal to zero. Mathematically, for any real number a, |a| ≥ 0.

Case 1: x + 2 ≥ 0
If x + 2 ≥ 0, then the absolute value of x + 2 will be equal to x + 2. The equation can be rewritten as x + 2 = -2. Solving this equation, we get:
x = -4

Case 2: x + 2 < />
If x + 2 < 0,="" then="" the="" absolute="" value="" of="" x="" +="" 2="" will="" be="" equal="" to="" -(x="" +="" 2),="" which="" is="" the="" negation="" of="" x="" +="" 2.="" the="" equation="" can="" be="" rewritten="" as="" -(x="" +="" 2)="-2." simplifying,="" we="" />
x + 2 = 2
x = 0

Final Analysis:
From the two cases we considered above, we see that the equation |x + 2| = -2 does not have a common solution for both cases. This implies that there is no value of x that satisfies the equation |x + 2| = -2.

Conclusion:
Therefore, the equation |x + 2| = -2 has no solution.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many...
Concept:
The Modulus Function '| |' is defined as:

Calculation:
Since the modulus function '||' always returns a positive value or 0, its not possible to have -2 as the value of modulus of any expression.
Hence, |x + 2| = -2 has no solution.
Explore Courses for SAT exam

Similar SAT Doubts

Directions:Each passage below is accompanied by a number of questions. For some questions, you will consider how the passage might be revised to improve the expression of ideas. For other questions, you will consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage or a question may be accompanied by one or more graphics (such as a table or graph) that you will consider as you make revising and editing decisions.Some questions will direct you to an underlined portion of a passage. Other questions will direct you to a location in a passage or ask you to think about the passage as a whole.After reading each passage, choose the answer to each question that most effectively improves the quality of writing in the passage or that makes the passage conform to the conventions of Standard Written English. Many questions include a "NO CHANGE" option. Choose that option if you think the best choice is to leave the relevant portion of the passage as it is.Question based on the following passage and supplementary material.The Eureka EffectYouve probably had the experience. After racking your brain for hours to solve a problem, you finally put it aside and move on to other things. Then, much later, seemingly out of(1) nowhere, perhapswhile showering or driving—the answer suddenly strikes you. Psychologists call this the “Eureka effect,” from the ancient Greek word meaning “I have found it,”(2) which Archimides is said to have shoutedas he ran naked from his bathtub through the streets of Syracuse upon suddenly solving a vexing physics problem.Does this feeling arise from our emotional centers or our cognitive centers? In other words, is it simply an emotional response to finding a solution, or does it(3) foretella fundamentally different way of thinking? Psychologists have tried to answer this question by looking inside subjects brains as they solve problems, using electroencephalograms (EEGs) and other tools.In one(4) experiment, subjectsperformed a word association task, scientists measured the activity in the region of the brain called the right hemisphere anterior superior temporal gyrus (RH aSTG). This region is known to be active in tasks, such as finding a theme in a story,(5) that requires integrating and bringing togetherinformation from many distant parts of the brain, but is not particularly active in emotional responses.The subjects were asked to perform a challenging verbal association task, press a button as soon as(6) solving it,and report whether or not they felt the “Aha!” feeling. If they did, the response was classified as an “insight” solution. If they did not, it was classified as a “non-insight” solution.(7) What was interesting, experimenters found that the insight solutions were accompanied by an elevated level of “gamma band” activity in the RH aSTG, supporting the theory that the feeling(8) had correspondedto a cognitive process rather than purely an emotional one.(9)Interpreting(10) this data isnot a very simple matter, however. Many questions remain to be answered. For instance, does the increased gamma-band activity represent a transition of cognitive processing from an unconscious state to a conscious one?(11) If that is true, a question would be what are the unconscious processes that are working? Also, in what way do those processes become conscious all of a sudden?Q. At this point in the passage, the author wants to mention specific evidence indicated by the graph. Which statement is most justified by the data in this graph?

Directions:Each passage below is accompanied by a number of questions. For some questions, you will consider how the passage might be revised to improve the expression of ideas. For other questions, you will consider how the passage might be edited to correct errors in sentence structure, usage, or punctuation. A passage or a question may be accompanied by one or more graphics (such as a table or graph) that you will consider as you make revising and editing decisions.Some questions will direct you to an underlined portion of a passage. Other questions will direct you to a location in a passage or ask you to think about the passage as a whole.After reading each passage, choose the answer to each question that most effectively improves the quality of writing in the passage or that makes the passage conform to the conventions of Standard Written English. Many questions include a "NO CHANGE" option. Choose that option if you think the best choice is to leave the relevant portion of the passage as it is.Question based on the following passage and supplementary material.The Eureka EffectYouve probably had the experience. After racking your brain for hours to solve a problem, you finally put it aside and move on to other things. Then, much later, seemingly out of(1) nowhere, perhapswhile showering or driving—the answer suddenly strikes you. Psychologists call this the “Eureka effect,” from the ancient Greek word meaning “I have found it,”(2) which Archimides is said to have shoutedas he ran naked from his bathtub through the streets of Syracuse upon suddenly solving a vexing physics problem.Does this feeling arise from our emotional centers or our cognitive centers? In other words, is it simply an emotional response to finding a solution, or does it(3) foretella fundamentally different way of thinking? Psychologists have tried to answer this question by looking inside subjects brains as they solve problems, using electroencephalograms (EEGs) and other tools.In one(4) experiment, subjectsperformed a word association task, scientists measured the activity in the region of the brain called the right hemisphere anterior superior temporal gyrus (RH aSTG). This region is known to be active in tasks, such as finding a theme in a story,(5) that requires integrating and bringing togetherinformation from many distant parts of the brain, but is not particularly active in emotional responses.The subjects were asked to perform a challenging verbal association task, press a button as soon as(6) solving it,and report whether or not they felt the “Aha!” feeling. If they did, the response was classified as an “insight” solution. If they did not, it was classified as a “non-insight” solution.(7) What was interesting, experimenters found that the insight solutions were accompanied by an elevated level of “gamma band” activity in the RH aSTG, supporting the theory that the feeling(8) had correspondedto a cognitive process rather than purely an emotional one.(9)Interpreting(10) this data isnot a very simple matter, however. Many questions remain to be answered. For instance, does the increased gamma-band activity represent a transition of cognitive processing from an unconscious state to a conscious one?(11) If that is true, a question would be what are the unconscious processes that are working? Also, in what way do those processes become conscious all of a sudden?Q. (6)

Top Courses for SATView all

Top Courses for SAT

The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer?
Question Description
The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer?.
Solutions for The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SAT. Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free.
Here you can find the meaning of The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The equation |x + 2| = -2 has:a)Unique solution.b)Two solutions.c)Many solutions.d)No solution.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice SAT tests.
Explore Courses for SAT exam

Top Courses for SAT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup