M L Aggarwal Solutions for Chapter: Linear Inequalities, Exercise 1: EXERCISE 7.1

Solve the inequality and show the graph of the solution on the number line:

$3\left(1-x\right)<2\left(x+4\right).$

Solve the inequality and show the graph of the solution on the number line.

$x+5\le 2x+3$

Solve the inequality and show the graph of the solution on the number line.

$\frac{4x-10}{3}\le \frac{5x-7}{2}$

Solve the inequality and show the graph of the solution on the number line :

$\frac{3x}{5}-\frac{2x-1}{3}>1$ 

Solve the inequality and show the graph of the solution on the number line :

$\frac{3x-4}{2}\ge \frac{x+1}{4}-1.$

The marks obtained by a student in two tests were $62$ and $48$. Find the number of minimum marks he should get in the third test to have an average of at least $60$ marks.

The marks obtained by Sukriti in first two unit tests are $75$ and $70$. Find the number of minimum marks she should get in the third unit test to have an average of at least $60$ marks.

The cost and revenue functions of a product are given by $C\left(x\right)=20x+4000$and $R\left(x\right)=60x+2000$ respectively, where $x$ is the number of items produced and sold. How many items must be sold to realise some profit.