Embibe Experts Solutions for Chapter: Linear Inequalities, Exercise 1: Exercise

Solve : $2\left(x-6\right)<3x-7, 11-2x<6-x$.

Solve : $5x-7<3\left(x+3\right), 1-\frac{3x}{2}\ge x-4$.

The solution set of $10x+24\le 34$, $x\in N$.

Set of values of $x$ satisfying the inequality $\frac{\sqrt{x+7}}{x+1}>\sqrt{3-x}$ is

A company manufactures cassettes. Its cost and revenue functions are $C\left(x\right)=26,000+30x$ and $R\left(x\right)=43x,$ respectively, where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit ?

The water acidity in a pool is considered normal when the average $pH$ reading of three daily measurements is between $8.2$ and $8.5$. If the first two $pH$ readings are $8.48$ and $8.35,$ find the range of $pH$ value for the third reading that will result in the acidity level being normal.

A solution is to be kept between ${40}^{°}\mathrm{C}$ and ${45}^{°}\mathrm{C}$. What is the range of temperature in degree Fahrenheit, if the conversion formula is $\mathrm{F}=\frac{9}{5}{ }^{\circ }C+{32}^{°}?$

The longest side of a triangle is twice the shortest side and the third side is $2 \mathrm{cm}$ Ionger than the shortest side. If the perimeter of the triangle is more than $166 \mathrm{cm}$, then find the minimum length of the shortest side(in cm).