Question

How do you write the inequality and solve given "twice a number increased by 3 is less than the number decreased by 4"?

Answer 1

Hint: Here, we will use the keyword of the phrase to write the expression in parts. We will then combine each part to form the required inequality. An Algebraic expression is defined as an expression which has both the numbers and the variables and the arithmetic operators like plus, minus, etc.

Complete Step by Step Solution:
Here, “a number” can be taken as \[x\].
Now we will simply take a few keywords of the statement and form the mathematical expression accordingly.
It is given as “twice a number” which means that it is times the assumed number. So, the mathematical expression is \[2x\].
Now as it is given that “twice a number increases by 3” which means that 3 is being added to twice a number. Therefore, the expression becomes \[2x + 3\].
Now as it is given that “twice a number increased by 3 is less than the number” which means that the previous expression is less than the assumed number. Therefore, the expression becomes
\[ \Rightarrow 2x + 3 < x\]
Now we will take the whole equation which states that “twice a number increased by 3 is less than the number decreased by 4" which means that subtraction of 4 in the right side of the previous expression. Therefore, we get the expression as
\[ \Rightarrow 2x + 3 < x - 4\]
Now we will solve the given inequality by taking the variable term on the one side and constants on the other side. Therefore, we get
\[ \Rightarrow 2x - x < - 4 - 3\]
\[ \Rightarrow x < - 7\]

Hence the mathematical expression for “twice a number increased by 3 is less than the number decreased by 4" is written as \[2x + 3 < x - 4\] and after solving this inequality we get \[x < - 7\].

Note:
We know that Arithmetic expression or Mathematical expression is defined as an expression with the numbers and the arithmetic operators like plus, minus etc. We have many ways to represent an algebraic expression into the word phrase. Word phrase is a way of representing the algebraic expression or mathematical expression in the form of sentences using the keywords. We should know that there is no single strategy for converting an algebraic expression into a word phrase and vice versa.