Question

How do you solve \[14p-8=22+20p\]?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will first take all constants to the left side of the equation. After that, we will take all terms having variable ‘p’ to the left side of the equation. After that, we will take the common term as 6 in the equation and try to remove that term. After solving the further equation, we will get the value of p.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to solve the equation \[14p-8=22+20p\]. We have to find the value of ‘p’ from the given equation in the question.
The given equation is
\[14p-8=22+20p\]
Firstly, we will take all the constants to the left side of the equation. After taking 22 to the left side of the equation, we can write the above equation as
\[\Rightarrow 14p-8-22=20p\]
The above equation can also be written as
\[\Rightarrow 14p-30=20p\]
Now, we will take the variable term that is ‘20p’ to the left side of the equation. we can write the above equation as
\[\Rightarrow 14p-20p-30=0\]
The above equation can also be written as
\[\Rightarrow -6p-30=0\]
Now, we will take out the common term that is -6 in the equation. The above equation can also be written as
\[\Rightarrow -6\left( p+5 \right)=0\]
Now, we will dive -6 the both side of the equation, we get
\[\Rightarrow \dfrac{-6\left( p+5 \right)}{-6}=\dfrac{0}{-6}\]
The above equation can also be written as
\[\Rightarrow \left( p+5 \right)=0\]
\[\Rightarrow p+5=0\]
Now, subtracting 5 to the both side of the equation, we will get
\[\Rightarrow p+5-5=0-5\]
The above equation can also be written as
\[\Rightarrow p=-5\]
Now, we have solved the equation \[14p-8=22+20p\] and have got the value of p as -5.

Note:
We should have a better knowledge in the topic of algebra to solve this type of question easily. If we want to check if our answer is correct or not, then we will cross-check our answer. We will substitute the value of x in the given equation.
The equation is
\[14p-8=22+20p\]
Putting the value of ‘p’ as -5 in the above equation, we get
\[\Rightarrow 14\left( -5 \right)-8=22+20\left( -5 \right)\]
We can write the above equation as
\[\Rightarrow -70-8=22-100\]
The above equation can also be written as
\[\Rightarrow -78=-78\]
Hence, we get that we have solved the equation and got the equation equal. So, we can say that our answer is correct.