06 रैखिक असमानताएँ
अभ्यास 2
Question:
Solve the following inequalities graphically in two-dimensional plane: 2x−3y>6
Answer:
Step 1: Rewrite the inequality in the form of y = mx + b, where m is the slope and b is the y-intercept.
2x - 3y > 6 => -3y > 6 - 2x => y > (2/3)x - 2
Step 2: Plot the line y = (2/3)x - 2 on the two-dimensional plane.
Step 3: Shade the side of the line that satisfies the inequality. The shaded side will be the solution.
Question:
Solve the following inequalities graphically in two-dimensional plane: y<−2
Answer:
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Draw a two-dimensional coordinate plane.
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Plot the inequality y < -2. This can be done by drawing a line on the coordinate plane with a slope of 0 and a y-intercept of -2.
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Shade the region below the line. This region represents the solution set of the inequality.
Question:
2x + y > 6
Answer:
Step 1: Subtract 2x from both sides of the equation to isolate y: y > 6 - 2x
Step 2: Divide both sides of the equation by the coefficient of y (in this case, 1): y > 6 - 2x ÷ 1 y > 6 - 2x
Question:
3x + 4y < 12
Answer:
- 3x + 4y < 12
- 3x < 12 - 4y
- x < (12 - 4y)/3
- x < 4 - (4/3)y
Question:
Solve the following inequalities graphically in two-dimensional plane: x>−3
Answer:
Step 1: Draw the graph of x-axis.
Step 2: Mark the point -3 on the x-axis.
Step 3: Draw a line from the point -3 on the x-axis to the right.
Step 4: Shade the area on the right side of the line. This area represents the solutions to the inequality.
Question:
Solve the following inequalities graphically in two-dimensional plane: x+y<5
Answer:
Step 1: Draw the graph.
Step 2: Plot the inequality line x+y=5.
Step 3: Shade the region below the line x+y=5.
Step 4: The region shaded is the solution of the inequality x+y<5.
Question:
Solve the following inequalities graphically in two-dimensional plane: −3x+2y≥−6
Answer:
Step 1: Rewrite the inequality as a function of y: y ≥ (3/2)x + 3
Step 2: Plot the equation on a two-dimensional plane.
Step 3: Shade the area on the graph that satisfies the inequality.
Step 4: The solution to the inequality is the shaded area.
Question:
-3x + 2y > -6
Answer:
Step 1: Subtract 2y from both sides of the inequality: -3x > -6 - 2y
Step 2: Divide both sides of the inequality by -3: x < 6/3 - (2/3)y
Question:
y + 8 > 2x
Answer:
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Subtract 8 from both sides: y > 2x - 8
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Divide both sides by 2: y/2 > x - 4
जेईई अध्ययन सामग्री (गणित)
01 सेट
02 संबंध एवं फलन
03 त्रिकोणमितीय फलन
04 गणितीय आगमन का सिद्धांत
05 सम्मिश्र संख्याएँ और द्विघात समीकरण
06 रैखिक असमानताएँ
07 क्रमचय और संचय
08 द्विपद प्रमेय
09 अनुक्रम और श्रृंखला
10 सीधी रेखाओं का अभ्यास
10 सीधी रेखाएँ विविध
11 शांकव खंड
12 त्रिविमीय ज्यामिति का परिचय
13 सीमाएं और डेरिवेटिव
14 गणितीय तर्क
15 सांख्यिकी
16 प्रायिकता