B. (14) पर भरा वृत्त और बाईं ओर छायांकन/Closed circle at (14) and shading left
Step 1
Concept
The sign \(\le\) includes (14) and smaller numbers are on the left. Use a closed circle for an included boundary.
Step 2
Why this answer is correct
The correct answer is B. (14) पर भरा वृत्त और बाईं ओर छायांकन / Closed circle at (14) and shading left. The sign \(\le\) includes (14) and smaller numbers are on the left. Use a closed circle for an included boundary.
Step 3
Exam Tip
\(\le\) में (14) शामिल है और उससे छोटी संख्याएँ बाईं ओर होती हैं। शामिल सीमा के लिए भरा वृत्त बनाइए।
A. (-12) और (-5) पर खाली वृत्त और बीच में छायांकन/Open circles at (-12) and (-5) with shading between
Step 1
Concept
Both sides have strict inequalities so both endpoints are excluded. The shaded region between them is the solution.
Step 2
Why this answer is correct
The correct answer is A. (-12) और (-5) पर खाली वृत्त और बीच में छायांकन / Open circles at (-12) and (-5) with shading between. Both sides have strict inequalities so both endpoints are excluded. The shaded region between them is the solution.
Step 3
Exam Tip
दोनों ओर कठोर असमता है इसलिए दोनों सीमाएँ शामिल नहीं हैं। बीच का छायांकित भाग समाधान है।
The open circle excludes (-13) and the right side has greater numbers. Hence the interval is (\(-13,\infty\)).
Step 2
Why this answer is correct
The correct answer is C. (\(-13,\infty\)). The open circle excludes (-13) and the right side has greater numbers. Hence the interval is (\(-13,\infty\)).
Step 3
Exam Tip
खाली वृत्त (-13) को बाहर रखता है और दाईं ओर बड़ी संख्याएँ होती हैं। इसलिए अंतराल (\(-13,\infty\)) है।
B. (-16) पर खाली वृत्त और बाईं ओर किरण/Open circle at (-16) and ray left
Step 1
Concept
In (\(-\infty,-16\)), (-16) is not included and smaller numbers are taken. So an open circle and left ray are drawn.
Step 2
Why this answer is correct
The correct answer is B. (-16) पर खाली वृत्त और बाईं ओर किरण / Open circle at (-16) and ray left. In (\(-\infty,-16\)), (-16) is not included and smaller numbers are taken. So an open circle and left ray are drawn.
Step 3
Exam Tip
(\(-\infty,-16\)) में (-16) शामिल नहीं है और छोटी संख्याएँ ली जाती हैं। इसलिए खाली वृत्त और बाईं किरण बनेगी।
B. (-9) बंद और (-2) खुला/(-9) closed and (-2) open
Step 1
Concept
(-9) has a square bracket so it is included and (-2) has a parenthesis so it is excluded. This decides the endpoints.
Step 2
Why this answer is correct
The correct answer is B. (-9) बंद और (-2) खुला / (-9) closed and (-2) open. (-9) has a square bracket so it is included and (-2) has a parenthesis so it is excluded. This decides the endpoints.
Step 3
Exam Tip
(-9) के साथ वर्ग कोष्ठक है इसलिए वह शामिल है और (-2) के साथ गोल कोष्ठक है इसलिए वह शामिल नहीं है। यही सिरों को तय करता है।
B. पूरी रेखा छायांकित और (7) पर खाली वृत्त/Whole line shaded with an open circle at (7)
Step 1
Concept
In \(x\ne 7\), all real numbers except (7) are included. The excluded value is shown by an open circle.
Step 2
Why this answer is correct
The correct answer is B. पूरी रेखा छायांकित और (7) पर खाली वृत्त / Whole line shaded with an open circle at (7). In \(x\ne 7\), all real numbers except (7) are included. The excluded value is shown by an open circle.
Step 3
Exam Tip
\(x\ne 7\) में (7) को छोड़कर सभी वास्तविक संख्याएँ शामिल हैं। छोड़े गए मान पर खाली वृत्त बनता है।
In \([-\frac{3}{2},2\)), \(-\frac{3}{2}\) is included but (2) is not. Therefore \(-\frac{3}{2}\) is a correct member.
Step 2
Why this answer is correct
The correct answer is C. -\(\frac{3}{2}\). In \([-\frac{3}{2},2\)), \(-\frac{3}{2}\) is included but (2) is not. Therefore \(-\frac{3}{2}\) is a correct member.
Step 3
Exam Tip
\([-\frac{3}{2},2\)) में \(-\frac{3}{2}\) शामिल है लेकिन (2) शामिल नहीं है। इसलिए \(-\frac{3}{2}\) सही सदस्य है।
The first part is the left side including (5), and the second part is the right side after (5). Together they give the whole number line.
Step 2
Why this answer is correct
The correct answer is B. सभी वास्तविक संख्याएँ / All real numbers. The first part is the left side including (5), and the second part is the right side after (5). Together they give the whole number line.
Step 3
Exam Tip
पहला भाग (5) सहित बाईं ओर है और दूसरा भाग (5) के बाद दाईं ओर है। दोनों मिलकर पूरी संख्या रेखा देते हैं।
Two separate parts are joined by \(\cup\). Both endpoints are excluded so parentheses are used.
Step 2
Why this answer is correct
The correct answer is B. (\(-\infty,-7\)\cup\(12,\infty\)). Two separate parts are joined by \(\cup\). Both endpoints are excluded so parentheses are used.
Step 3
Exam Tip
दो अलग हिस्सों को \(\cup\) से जोड़ा जाता है। दोनों सीमाएँ शामिल नहीं हैं इसलिए गोल कोष्ठक लगेंगे।
In \(x<-\frac{9}{4}\), the boundary is excluded and smaller numbers are included. Hence (\(-\infty,-\frac{9}{4}\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-\frac{9}{4}\)). In \(x<-\frac{9}{4}\), the boundary is excluded and smaller numbers are included. Hence (\(-\infty,-\frac{9}{4}\)) is correct.
Step 3
Exam Tip
\(x<-\frac{9}{4}\) में सीमा शामिल नहीं है और उससे छोटी संख्याएँ आती हैं। इसलिए (\(-\infty,-\frac{9}{4}\)) सही है।
The strict sign (>) does not include \(\frac{7}{3}\). Therefore an open circle is drawn at the boundary.
Step 2
Why this answer is correct
The correct answer is B. खाली वृत्त / Open circle. The strict sign (>) does not include \(\frac{7}{3}\). Therefore an open circle is drawn at the boundary.
Step 3
Exam Tip
कठोर (>) में \(\frac{7}{3}\) शामिल नहीं होता। इसलिए सीमा पर खाली वृत्त बनेगा।
B. \(\frac{2}{3}\) बंद और \(\frac{8}{3}\) खुला होगा/\(\frac{2}{3}\) closed and \(\frac{8}{3}\) open
Step 1
Concept
The square bracket includes \(\frac{2}{3}\), and the parenthesis excludes \(\frac{8}{3}\). So the first endpoint is closed and the second is open.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2}{3}\) बंद और \(\frac{8}{3}\) खुला होगा / \(\frac{2}{3}\) closed and \(\frac{8}{3}\) open. The square bracket includes \(\frac{2}{3}\), and the parenthesis excludes \(\frac{8}{3}\). So the first endpoint is closed and the second is open.
Step 3
Exam Tip
वर्ग कोष्ठक \(\frac{2}{3}\) को शामिल करता है और गोल कोष्ठक \(\frac{8}{3}\) को बाहर रखता है। इसलिए पहला सिरा बंद और दूसरा खुला होगा।
Both closed endpoints show that both boundaries are included. So inclusive inequalities are used on both sides.
Step 2
Why this answer is correct
The correct answer is D. \(18\le x\le 25\). Both closed endpoints show that both boundaries are included. So inclusive inequalities are used on both sides.
Step 3
Exam Tip
दोनों बंद सिरे बताते हैं कि दोनों सीमाएँ शामिल हैं। इसलिए दोनों ओर बराबरी सहित असमता होगी।
A. (-22) पर भरा वृत्त और बाईं ओर तीर/Closed circle at (-22) and arrow left
Step 1
Concept
In \(x\le -22\), (-22) is included and smaller numbers are taken. So a closed circle with a left arrow is used.
Step 2
Why this answer is correct
The correct answer is A. (-22) पर भरा वृत्त और बाईं ओर तीर / Closed circle at (-22) and arrow left. In \(x\le -22\), (-22) is included and smaller numbers are taken. So a closed circle with a left arrow is used.
Step 3
Exam Tip
\(x\le -22\) में (-22) शामिल है और उससे छोटी संख्याएँ ली जाती हैं। इसलिए भरा वृत्त बाईं ओर तीर के साथ होगा।
B. \(x\le -6\) या \(x\ge 10\)/\(x\le -6\) or \(x\ge 10\)
Step 1
Concept
The first part gives \(x\le -6\) and the second gives \(x\ge 10\). The symbol \(\cup\) shows the union of both parts.
Step 2
Why this answer is correct
The correct answer is B. \(x\le -6\) या \(x\ge 10\) / \(x\le -6\) or \(x\ge 10\). The first part gives \(x\le -6\) and the second gives \(x\ge 10\). The symbol \(\cup\) shows the union of both parts.
Step 3
Exam Tip
पहला भाग \(x\le -6\) और दूसरा भाग \(x\ge 10\) देता है। \(\cup\) दोनों भागों का मिलन दिखाता है।
A. सिर्फ (-14) पर भरा बिंदु/Only a closed point at (-14)
Step 1
Concept
A closed interval with equal endpoints includes only that number. Therefore a closed point is drawn at (-14).
Step 2
Why this answer is correct
The correct answer is A. सिर्फ (-14) पर भरा बिंदु / Only a closed point at (-14). A closed interval with equal endpoints includes only that number. Therefore a closed point is drawn at (-14).
Step 3
Exam Tip
समान सीमाओं वाला बंद अंतराल केवल उसी संख्या को शामिल करता है। इसलिए (-14) पर भरा बिंदु बनेगा।
\(\le\) includes the boundary \(\frac{5}{6}\) and takes numbers to the left. Therefore (\(-\infty,\frac{5}{6}]\) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,\frac{5}{6}]\). \(\le\) includes the boundary \(\frac{5}{6}\) and takes numbers to the left. Therefore (\(-\infty,\frac{5}{6}]\) is correct.
Step 3
Exam Tip
\(\le\) सीमा \(\frac{5}{6}\) को शामिल करता है और बाईं ओर की संख्याएँ लेता है। इसलिए (\(-\infty,\frac{5}{6}]\) सही है।
B. (x=-4) समाधान में नहीं है/(x=-4) is not in the solution
Step 1
Concept
An open circle keeps the boundary out of the solution. Therefore (x=-4) is not included.
Step 2
Why this answer is correct
The correct answer is B. (x=-4) समाधान में नहीं है / (x=-4) is not in the solution. An open circle keeps the boundary out of the solution. Therefore (x=-4) is not included.
Step 3
Exam Tip
खुला वृत्त सीमा को समाधान से बाहर रखता है। इसलिए (x=-4) शामिल नहीं है।
A. पहले में दोनों सिरे खुले और दूसरे में दोनों सिरे बंद/The first has both endpoints open and the second has both endpoints closed
Step 1
Concept
Parentheses exclude endpoints and square brackets include endpoints. This creates the endpoint difference on the number line.
Step 2
Why this answer is correct
The correct answer is A. पहले में दोनों सिरे खुले और दूसरे में दोनों सिरे बंद / The first has both endpoints open and the second has both endpoints closed. Parentheses exclude endpoints and square brackets include endpoints. This creates the endpoint difference on the number line.
Step 3
Exam Tip
गोल कोष्ठक सीमाओं को बाहर रखता है और वर्ग कोष्ठक सीमाओं को शामिल करता है। यही संख्या रेखा पर सिरों का अंतर बनाता है।
(\(-\infty,\infty\)) represents all real numbers. Therefore the entire number line is shaded.
Step 2
Why this answer is correct
The correct answer is C. पूरी संख्या रेखा / The entire number line. (\(-\infty,\infty\)) represents all real numbers. Therefore the entire number line is shaded.
Step 3
Exam Tip
(\(-\infty,\infty\)) सभी वास्तविक संख्याओं को दर्शाता है। इसलिए पूरी संख्या रेखा छायांकित होगी।
Outward shading shows two separate parts and open circles exclude the boundaries. Hence (\(-\infty,-4\)\cup\(11,\infty\)) is correct.
Step 2
Why this answer is correct
The correct answer is B. (\(-\infty,-4\)\cup\(11,\infty\)). Outward shading shows two separate parts and open circles exclude the boundaries. Hence (\(-\infty,-4\)\cup\(11,\infty\)) is correct.
Step 3
Exam Tip
बाहर की छायांकन दो अलग भाग दिखाती है और खुले वृत्त सीमाओं को बाहर रखते हैं। इसलिए (\(-\infty,-4\)\cup\(11,\infty\)) सही है।
B. \(\frac{4}{5}\) पर एक भरा बिंदु/One closed point at \(\frac{4}{5}\)
Step 1
Concept
A closed interval with equal endpoints includes only that number. Therefore one closed point is drawn at \(\frac{4}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{4}{5}\) पर एक भरा बिंदु / One closed point at \(\frac{4}{5}\). A closed interval with equal endpoints includes only that number. Therefore one closed point is drawn at \(\frac{4}{5}\).
Step 3
Exam Tip
समान सीमाओं वाला बंद अंतराल केवल उसी संख्या को शामिल करता है। इसलिए \(\frac{4}{5}\) पर एक भरा बिंदु बनेगा।
The closed circle includes \(-\frac{5}{2}\), and greater numbers lie to the right. Therefore \(x\ge -\frac{5}{2}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\ge -\frac{5}{2}\). The closed circle includes \(-\frac{5}{2}\), and greater numbers lie to the right. Therefore \(x\ge -\frac{5}{2}\) is correct.
Step 3
Exam Tip
भरा वृत्त \(-\frac{5}{2}\) को शामिल करता है और दाईं ओर बड़ी संख्याएँ होती हैं। इसलिए \(x\ge -\frac{5}{2}\) सही है।
A. समाधान में शामिल है/It is included in the solution
Step 1
Concept
The square bracket includes (7) in the solution. Therefore a closed circle is drawn at (7).
Step 2
Why this answer is correct
The correct answer is A. समाधान में शामिल है / It is included in the solution. The square bracket includes (7) in the solution. Therefore a closed circle is drawn at (7).
Step 3
Exam Tip
वर्ग कोष्ठक (7) को समाधान में शामिल करता है। इसलिए (7) पर भरा वृत्त बनेगा।
The closed endpoint includes (2), and the open endpoint excludes (9). Therefore the correct inequality is \(2\le x<9\).
Step 2
Why this answer is correct
The correct answer is D. \(2\le x<9\). The closed endpoint includes (2), and the open endpoint excludes (9). Therefore the correct inequality is \(2\le x<9\).
Step 3
Exam Tip
बंद सिरा (2) को शामिल करता है और खुला सिरा (9) को बाहर रखता है। इसलिए सही असमता \(2\le x<9\) है।
