Question

How do you solve \[9(p - 4) = 18\]?

Answer 1

Hint: Solve the given equation i.e. first multiply all the terms outside the bracket with terms inside the bracket. Then bring all variable values together on one side and all constant values together on the other side. Cancel possible terms and write the equation in simplest form. In the end the equation will give the value of ‘p’ being equal to constant.

Complete step-by-step solution:
We are given the equation \[9(p - 4) = 18\]
Since the equation has only one variable i.e. p, we will calculate the value of p.
We have value 9 outside the bracket, so we multiply the numbers outside the bracket with the terms inside the bracket.
\[ \Rightarrow 9 \times p - 9 \times 4 = 18\]
Calculate each of the products on left hand side of the equation
\[ \Rightarrow 9p - 36 = 18\]
Shift all constant values to the right hand side of the equation.
\[ \Rightarrow 9p = 18 + 36\]
Calculate the value on right hand side of the equation
\[ \Rightarrow 9p = 54\]
Cancel same factors from both sides of the equation i.e. 9
\[ \Rightarrow p = 6\]

\[\therefore \]Solution of the equation \[9(p - 4) = 18\] is \[p = 6\]

Note: Many students try to solve the equation by substituting values of ‘p’ one by one, which is wrong as we have only one variable i.e. p and if we substitute its value we will not get the value of any other variable. Keep in mind the same values can be cancelled from both sides of the equation directly or can be brought to one side of the equation and then subtracted. Also, keep in mind when shifting values from one side of the equation to another side of the equation, always change sign from positive to negative and vice-versa.
Alternate method:
We can directly cancel the same factor i.e. 9 from both sides of the equation \[9(p - 4) = 18\]
\[ \Rightarrow (p - 4) = 2\]
Shift constant value to right hand side of the equation
\[ \Rightarrow p = 2 + 4\]
Add the terms on right hand side of the equation
\[ \Rightarrow p = 6\]
\[\therefore \]Solution of the equation \[9(p - 4) = 18\] is \[p = 6\]