Linear Inequalities Exercise 2
Question:
Solve the following inequalities graphically in twodimensional 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 yintercept.
2x  3y > 6 => 3y > 6  2x => y > (2/3)x  2
Step 2: Plot the line y = (2/3)x  2 on the twodimensional 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 twodimensional plane: y<−2
Answer:

Draw a twodimensional coordinate plane.

Plot the inequality y < 2. This can be done by drawing a line on the coordinate plane with a slope of 0 and a yintercept of 2.

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 twodimensional plane: x>−3
Answer:
Step 1: Draw the graph of xaxis.
Step 2: Mark the point 3 on the xaxis.
Step 3: Draw a line from the point 3 on the xaxis 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 twodimensional 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 twodimensional 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 twodimensional 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:

Subtract 8 from both sides: y > 2x  8

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