Question

a.
(5p + 2) - (16/3p + 1)=8​

Answer 1

Answer:

p = -21

Step-by-step explanation:

As per the provided information in the given question, we have to solve for the variable p.

In order to solve this equation, we'll be using the transposition method.

• This is the method used to solve a linear equation having variables and constants.
• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\longmapsto \rm { (5p + 2) - \Bigg ( \dfrac{16}{3}p + 1\Bigg ) = 8}$

Step 1 : Removing the brackets. Since there is a minus sign before the bracket, so the signs of the numbers in the brackets will get changed.

$\longmapsto \rm { 5p + 2 - \dfrac{16}{3}p -1 = 8}$

Step 2 : Grouping all the like terms.

$\longmapsto \rm { 5p - \dfrac{16}{3}p +2 -1 = 8}$

Step 3 : Performing subtraction in L.H.S.

$\longmapsto \rm { 5p - \dfrac{16}{3}p +1 = 8}$

Step 4 : Taking the L.C.M and making the denominator same in order to perform addition.

$\longmapsto \rm { \dfrac{15p -16p}{3} +1 = 8}$

Step 5 : Performing subtraction in L.H.S and transposing 1 from L.H.S. to R.H.S.

$\longmapsto \rm { \dfrac{-p}{3} = 8-1}$

Step 6 : Performing subtraction in R.H.S.

$\longmapsto \rm { \dfrac{-p}{3} = 7}$

Step 7 : Transposing 3 from L.H.S to R.H.S.

$\longmapsto \rm { -p = 7\times 3}$

Step 8 : Performing multiplication in R.H.S.

$\longmapsto \rm { -p = 21}$

Step 9 : Multiplying (-1) on both sides to balance the equation.

$\longmapsto \rm { (-1)-p = (-1)21}$

$\longmapsto \bf { p = -21}$

∴ Value of p is -21.