Translating a Sentence into a One-Step Inequapty

We have already been introduced to inequapties, which show the relationship between two quantities that are not equal. Here sentences are given, which need to be translated into one-step inequapties.

Rules to write one-step inequapties

A sentence generally has three parts, the left, the middle and the right ones.

We proceed from the left part, which usually contains the variable and translate into an expression.

We write the inequapty sign from the middle one.

We then write the expression for the right part of the sentence, which is usually a number.

The examples below explain the above rules

Nine subtracted from b is greater than or equal to −21

Solution

Step 1:

We start from the left and proceed towards the right

On the left, there is ‘9 subtracted from b’ and on the right, there is ‘−21’ and the inequapty ‘greater than or equal to’ in the middle

Step 2:

‘Nine subtracted from b’ translates to b − 9

So, the statement “Nine subtracted from b is greater than or equal to −21” translates to

b −9 ≥ −21

Seven more than ‘a’ is less than or equal to 18

Solution

Step 1:

We start from the left and proceed towards the right

On the left, there is ‘7 more than ‘a’ ’ and on the right, there is ‘18’ and the inequapty ‘less than or equal to’ in the middle

Step 2:

‘Seven more than from ‘a’ translates to a + 7

So, the statement “Seven added to a is less than or equal to 18” translates to

a + 7 ≤ 18