Advertisements
Advertisements
Question
Solve the inequalities and represent the solution graphically on number line:
5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47
Advertisements
Solution
5(2x – 7) – 3(2x + 3) ≤ 0
⇒ 10x – 35 – 6x – 9 ≤ 0
⇒ 4x – 44 ≤ 0
⇒ 4x ≤ 44
⇒ x ≤ 11 …(1)
2x + 19 ≤ 6x + 47
⇒ 19 – 47 ≤ 6x – 2x
⇒ –28 ≤ 4x
⇒ –7 ≤ x …(2)
From (1) and (2), it can be concluded that the solution set for the given system of inequalities is [–7, 11]. The solution of the given system of inequalities can be represented on number line as
APPEARS IN
RELATED QUESTIONS
Solve the given inequality graphically in two-dimensional plane: x + y < 5
Solve the given inequality graphically in two-dimensional plane: 3x + 4y ≤ 12
Solve the given inequality graphically in two-dimensional plane: y + 8 ≥ 2x
Solve the given inequality graphically in two-dimensional plane: x – y ≤ 2
Solve the given inequality graphically in two-dimensional plane: 2x – 3y > 6
Solve the given inequality graphically in two-dimensional plane: 3y – 5x < 30
Solve the given inequality graphically in two-dimensional plane: x > –3
Solve the inequalities and represent the solution graphically on number line:
5x + 1 > –24, 5x – 1 < 24
Solve the inequality and represent the solution graphically on number line:
2(x – 1) < x + 5, 3(x + 2) > 2 – x
A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by `F= 9/8` C + 32?
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
Solve the following systems of linear inequations graphically:
x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
Solve the following systems of linear inequations graphically:
x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
Solve the following systems of linear inequations graphically:
2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0
Show that the solution set of the following linear inequations is empty set:
x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0
Show that the solution set of the following linear inequations is empty set:
x + 2y ≤ 3, 3x + 4y ≥ 12, y ≥ 1, x ≥ 0, y ≥ 0
Find the linear inequations for which the shaded area in Fig. 15.41 is the solution set. Draw the diagram of the solution set of the linear inequations:
Show that the solution set of the following linear in equations is an unbounded set:
x + y ≥ 9
3x + y ≥ 12
x ≥ 0, y ≥ 0
Solve the following systems of inequations graphically:
12x + 12y ≤ 840, 3x + 6y ≤ 300, 8x + 4y ≤ 480, x ≥ 0, y ≥ 0
Solve the following systems of inequations graphically:
x + 2y ≤ 40, 3x + y ≥ 30, 4x + 3y ≥ 60, x ≥ 0, y ≥ 0
Show that the solution set of the following system of linear inequalities is an unbounded region:
\[2x + y \geq 8, x + 2y \geq 10, x \geq 0, y \geq 0\]
Mark the correct alternative in each of the following:
If x\[<\]7, then
Write the solution of the inequation\[\frac{x^2}{x - 2} > 0\]
Find the linear inequalities for which the shaded region in the given figure is the solution set.
State which of the following statement is True or False.
If x < y and b < 0, then `x/"b" < y/"b"`
State which of the following statement is True or False.
If xy > 0, then x < 0 and y < 0
Graph of x < 3 is
Graph of x ≥ 0 is
Graph of y ≤ 0 is
