Question

How do you solve \[3p-6>21\]?

Answer 1

Hint: This type of problem is based on the concept of inequality. First, we have to make some necessary changes to the given function \[3p-6>21\] and obtain 3p in the left-hand side of the equation. Then, we should divide the function by 3 to obtain p alone on the left-hand side of the function. Therefore, we get the required solution of the given inequality.

Complete step by step answer:
According to the question, we are asked to find the solution to the given function \[3p-6>21\].
We have been given the function \[3p-6>21\]. -----(1)
We first have to add 6 on both sides of equation (1).
Therefore, we get,
\[\Rightarrow 3p-6+6>21+6\]
And we know that the same terms with opposite signs cancel out.
Therefore, we get,
\[\Rightarrow 3p>27\] ---------(2)
Now let us divide equation (2) by 3.
We get,
 \[\frac{3p}{3}>\frac{27}{3}\]
We know that, \[27=3\times 9\].
Therefore, using this in the above obtained inequality, we get
 \[\frac{3p}{3}>\frac{3\times 9}{3}\]
On cancelling out the common terms in the above inequality, we get,
\[\Rightarrow p>\frac{27}{3}\]
On further simplifications, we get,
\[p>9\]
Therefore,
\[p>9\]
Hence, the exact value of p in \[3p-6>21\] is \[p>9\].

Note:
Whenever you get this type of problem, we should always try to make the necessary changes in the given function to get the final of the function which will be the required answer. We should avoid calculation mistakes based on sign conventions. We should always take ‘p’ to the left-hand side of the equation and then solve. We can also solve this type of problem by cross-multiplying the given inequality. Similarly, we can find the solution of \[5p+17<3\] the exact same way.