Solve the inequalities and represent the solution graphically on number line: 5(2x –7) – 3(2x+3) ≤ 0, 2x+19 ≤ 6x+47.
Solution and Explanation
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
Top Questions on Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- Solve the given inequality and show the graph of the solution on number line: 3(1 - x) < 2(x + 4).
- CBSE Class XI
- Mathematics
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- 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?
- CBSE Class XI
- Mathematics
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- Solve the following inequalities and represent the solution graphically on number line: 3x –7 > 2(x-6), 6-x > 11-2x.
- CBSE Class XI
- Mathematics
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- Solve the inequalities and represent the solution graphically on number line: 2(x–1) < x+5, 3(x+2) > 2-x.
- CBSE Class XI
- Mathematics
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
- Solve the inequalities and represent the solution graphically on number line: 5x + 1 > – 24, 5x – 1 < 24.
- CBSE Class XI
- Mathematics
- Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
Questions Asked in CBSE Class XI exam
- Draw formulas for the first five members of each homologous series beginning with the following compounds.\((a) H–COOH (b) CH_3COCH_3 (c) H–CH=CH_2\)
- CBSE Class XI
- Organic Chemistry- Some Basic Principles and Techniques
- Distinguish between the following pairs of sentences.
(i) He was visibly moved.
(ii) He was visually impaired.- CBSE Class XI
- The adventure
- How, according to you, can peace and liberty be maintained in a state?
- CBSE Class XI
- The tale of melon City
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- CBSE Class XI
- Pressure
- Describe the change in hybridisation (if any) of the Al atom in the following reaction.
\(AlCl_3+Cl^- \rightarrow AlCl_4^-\)- CBSE Class XI
- Hybridisation
Concepts Used:
Inequalities
In mathematics, inequality is a relationship that compares two numbers or other mathematical expressions in a non-equal fashion. It is most commonly used to compare the size of two numbers on a number line.
Specifically, a linear inequality is a mathematical inequality that integrates a linear function. One of the symbols of inequality is observed in a linear inequality: In graph form, it represents data that is not equal.
Some of the linear inequality symbols are given below:
- < less than
- > greater than
- ≤ less than or equal to
- ≥ greater than or equal to
- ≠ not equal to
- = equal to
Inequalities can be demonstrated as questions that are solved using alike procedures to equations, or as statements of fact in the form of theorems. It is used to contrast numbers and find the range or ranges of values that pleases a variable's criteria.