Question

How do you find the numbers such that four less than half the number is at least five and at most ten ?

Answer 1

Hint: Here in this question, we have to read the question and find the relation by reading the question. By knowing the relation, we can have to write in the form of numerals. While writing in the numeral form we use the variables, constants and arithmetic operations and simplify the inequality.


Complete step by step solution:
The algebraic expression or equation is a combination of variables and constants. The variables are alphabets and the constants are numerals. In the algebraic expression we have 3 different types and they are monomial, binomial and polynomial. The algebraic expression or equation involves the arithmetic operations.

We have some sentences, by reading the sentences we have to use arithmetic operations.
-If the sentence involves a plus b, the sum of a and b, a increased by b, b more than a, the total of a and b, b added to a then we use the addition arithmetic operation.
-If the sentences involve a minus b, the difference of a and b, b subtracted from a, a decreased by b, b less than a then we use the subtraction arithmetic operation.
-If the sentence involves a times b, the product of a and b then we use the multiplication arithmetic operation. And so on.

Now let us go through the question, in the question we have the numbers such that four less than half the number is at least five and at most ten, in this sentence we have less than word so we use the subtraction arithmetic operation. So, we write it as
\[5 \leqslant \dfrac{x}{2} - 4 \leqslant 10\]
Now we have to simplify the above inequality. Now add 4 to the above inequality we have
\[ \Rightarrow 5 + 4 \leqslant \dfrac{x}{2} - 4 + 4 \leqslant 10 + 4\]
On simplifying we have
\[ \Rightarrow 9 \leqslant \dfrac{x}{2} \leqslant 14\]
now multiply the above inequality by 2 we have
\[ \Rightarrow 9 \times 2 \leqslant \dfrac{x}{2} \times 2 \leqslant 14 \times 2\]
On simplifying we have
\[ \Rightarrow 18 \leqslant x \leqslant 28\]

Therefore, the numbers will be from 18 to 28.

Note: The algebraic expression or equation can be converted or transformed into a phrase form. The phrase form is converted or transformed into the numeral form. While converting or transforming the phrase form into numeral form we use variable, numbers and the arithmetic operations.