Question

How do you solve $3b-7<32$ ?

Answer 1

Hint: For solving this equation, first of all we should be aware of Inequalities. In mathematics, an inequality is a relation which compares two values, showing if one is greater than, less than or equal to the other value.

Complete step by step answer:
An inequality is just a non-equal comparison between the two numbers or the mathematical expressions. For example:-
$a \ne b$ This suggests that in this case a is not equal to b.
$a < b$ This suggests that in this case b is greater than a.
$a > b$ This suggests that in this case a is greater than b.
$a \leqslant b$ This suggests that in this case b is greater than or equal to a.
$a \geqslant b$ This suggests that in this case a is greater than or equal to b.

There are four types of inequalities. These are as follows:-
1. Strict - The equation having the $ < or > $ symbol between R.H.S and L.H.S are termed as strict inequalities.
2. Slack - The equation having the $ \leqslant or \geqslant $ symbol between R.H.S and L.H.S are termed as Slack inequalities.
3. Linear - The equations which have the degree as one are termed as linear inequalities.
Eg: $2x + 3y > 6$
4. Quadratic - The equations which have the degree as two are termed as the quadratic inequalities.
Eg: $7{x^2} + 5y > 16$

Now we will solve the given equation $3b - 7 < 32$ ………….$\left( i \right)$ eq
Adding 7 on both side in the eq $\left( i \right)$ we get
$3b - 7 + 7 < 32 + 7or3b < 39$
Now dividing both sides by 3 we get $\dfrac{{3b}}{3} < \dfrac{{39}}{3}orb < 3$.

Hence the required answer for the equation $3b - 7 < 32$ is $b < 3$.

Note: The use of inequalities in math is to compare the relative size of values. They are used to compare variables, integers and various other algebraic expressions. The linear inequalities are used to solve the problems in different fields like engineering, mathematics, science and so on.