Relational open sentences: An open sentence, which have relational operators are called as a relational open sentences like 2 + 4y < 6.

Arithmetic open sentences: Open sentences, which have arithmetic operators like addition, subtraction, multiplication and division, are called as arithmetic open sentences,

Like x + 3 = 8.

Now we discuss how we solving open sentences:

For solving open sentences, we use following steps -

Step 1: First of all, we check what kind of open sentences we have like we have relational open sentences or we have arithmetic open sentences.

Step 2: In relational open sentences, we use number line to perform these open sentences like for solving the 2 + 4y < 6, we simplify the equation -

2 + 4y < 6,

=> 4y < 6 – 2,

=> 4y < 4,

=> y < 1,

Now we make number line for y < 1, means all number less than 1 on number line are answer of these open sentences.

Step 3: For solving the arithmetic open sentences, we put value, if it satisfy the equation, then our open sentences are true unless it is a false sentence like we have an open sentence, x + 3 = 8.

Now we solve this equation -

x + 3 = 8,

=> x = 8 – 3,

=> x = 5,

Now we check true or false -

x + 3 = 8,

Now put x = 5

=> 5 + 3 = 8 = r h s

So, l h s = r h s

Therefore x + 3 = 8 is an open sentence, which produces true result for x = 5.