06 Linear Inequalities

Exercise 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:

  1. Draw a two-dimensional coordinate plane.

  2. 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.

  3. 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:

  1. 3x + 4y < 12
  2. 3x < 12 - 4y
  3. x < (12 - 4y)/3
  4. 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:

  1. Subtract 8 from both sides: y > 2x - 8

  2. Divide both sides by 2: y/2 > x - 4

Back To Study Material

JEE NCERT Solutions (Mathematics)

01 Sets

02 Relations and Functions

03 Trigonometric Functions

04 Principle of Mathematical Induction

05 Complex Numbers and Quadratic Equations

06 Linear Inequalities

07 Permutations and Combinations

08 Binomial Theorem

09 Sequences and Series

10 Straight Lines Exercise

10 Straight Lines Miscellaneous

11 Conic Sections

12 Introduction to Three Dimensional Geometry

13 Limits and Derivatives

14 Mathematical Reasoning

15 Statistics

16 Probability

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