Question

How do you write an equality and the given “sum of nine times a number and 15 is less than or equal to the sum of 24 and 10 times number”?

Answer 1

Hint: The above problem is based on the concept of inequality equations.
In equality is a relation who makes a non-equal comparison between two numbers or other mathematical expressions.
Using the sign conventions of the inequality we will write the equation.

Complete step-by-step solution:
Let’s discuss some points about inequality and then we will do the calculation part of the problem.
An inequality is a relation which makes a non- equal comparison between two numbers or other mathematical expressions. It is most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities.
Now, we will form the inequality equation as the given questions.
Sum of nine times a number and 15 less than or equal to the sum of 24 and 10 times the same unknown number.
$ \Rightarrow 9x + 15 \leqslant 24 + 10x$ (Given inequality, we have framed according to the statement of the question)
In order to solve the inequality add or subtract the numbers on either RHS or LHS.
$ \Rightarrow 9x + 15 - 9x \leqslant 24 + 10x - 9x$ (We have subtracted 9x from both the sides)
$ \Rightarrow 15 \leqslant 24 + x$ (Now we will subtract 24 from both sides)
$ \Rightarrow 15 - 24 \leqslant 24 + x - 24$ (only the constant term and x will be left)
$ \Rightarrow - 9 \leqslant x$ (Our inequality becomes)

Therefore the required inequality is $- 9 \leqslant x$.

Note: Inequalities have many applications such as used in the system of linear Inequalities, used in various engineering subjects as well as in control system inequalities are used to determine the stability o f the system available to us, to determine the maximum and minimum value of the system.