Algebraic Solutions of Linear Inequalities in One Variable and Their Graphical Representation

How many litres of water will have to be added to $1125$ litres of the $45\%$ solution of acid so that the resulting mixture will contain more than $25\%$ but less than $30\%$ acid content?

A man wants to cut three lengths from a single piece of board of length $91 \mathrm{c}\mathrm{m}$. The second length is to be $3 \mathrm{c}\mathrm{m}$ longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least $5 \mathrm{c}\mathrm{m}$ longer than the second?

The longest side of a triangle is $3$ times the shortest side and the third side is $2 \mathrm{c}\mathrm{m}$ shorter than the longest side. If the perimeter of the triangle is at least $61 \mathrm{c}\mathrm{m}$, find the minimum length of the shortest side.

Find all pairs of consecutive even positive integers, both of which are larger than $5$ such that their sum is less than $23.$

Find all pairs of consecutive odd positive integers both of which are smaller than $10$ such that their sum is more than $11.$

To receive Grade $\mathrm{‘}\mathrm{A}\mathrm{’}$ in a course, one must obtain an average of $90$ marks or more in five examinations (each of $100$ marks). If Sunita’s marks in first four examinations are $87,92,94$ and $95,$ find minimum marks that Sunita must obtain in fifth examination to get grade $\mathrm{‘}\mathrm{A}\mathrm{’}$ in the course.

Ravi obtained $70$ and $75$ marks in first two unit test. Find the minimum marks he should get in the third test to have an average of at least $60$ marks.

Solve the given inequality and show the graph of the solution on number line:
$\frac{x}{2}\ge \frac{\left(5x-2\right)}{3}-\frac{\left(7x-3\right)}{5}$

Solve the given inequality and show the graph of the solution on number line:
$3\left(1-x\right)<2\left(x+4\right)$

Solve the given inequality and show the graph of the solution on number line.
$5x-3\ge 3x-5$

Solve the given inequality and show the graph of the solution on number line: $3x-2<2x+1$

Solve the given inequality for real $x:$
$\frac{(2x-1)}{3}\ge \frac{(3x-2)}{4}-\frac{(2-x)}{5}$

Solve the given inequality for real $x:$
$\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$.

Solve the given inequality for real $x:37-(3x+5)\ge 9x-8(x-3)$

Solve the given inequality for real $x:$
$2(2x+3)-10<6(x-2)$

Solve the given inequality for real $x:$ $\frac{1}{2}\left(\frac{3x}{5}+4\right)\ge \frac{1}{3}(x-6)$

Solve the given inequality for real $x:$
$\frac{3\left(x-2\right)}{5}\le \frac{5\left(2-x\right)}{3}$

Solve the given inequality for real $x:$
$\frac{x}{3}>\frac{x}{2}+1$

Solve the given inequality for real $x:$
$x+\frac{x}{2}+\frac{x}{3}<11$

Solve the given inequality for real $x:$
$3(2–x)\ge 2(1–x)$