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