Question

How do you solve the equation \[22 = - 11k\]?

Answer 1

Hint: In an equation if we either add or subtract any number on both sides of the equation then the resulting equation is still true. Same is true for multiply and division except the number zero.

Complete step-by-step solution:
The given equation is \[22 = - 11k\].
We have to find the value of \[k\] to solve the given equation \[22 = - 11k\].
Here, on the left hand side of the equation has only one term which is \[22\] and similarly on the right hand side of the equation has only one term which is \[ - 11k\].
According to the given equation, the number \[22\]is equal to the negative of the product of number \[11\] and \[k\].
It is equivalent to the equation that the negative of the product of a number \[11\] and \[k\] is equal to the number \[22\].
\[ - 11k = 22\]
Also we can write number \[22\] as the product of numbers \[2\] and \[11\] therefore split the right hand side of the equation as shown below.
\[ \Rightarrow - 11k = 2 \times 11\]
Similarly we can write \[ - 11k\] as the product of numbers \[ - 1\], \[11\] and \[k\] therefore split the left hand side of the equation as shown below.
\[ \Rightarrow - 1 \times 11 \times k = 2 \times 11\]
So, both sides have the number \[11\] as a multiplication. Divide both sides by the number \[11\] and the resultant equation still true as shown below.
\[ \Rightarrow \dfrac{{ - 1 \times 11 \times k}}{{11}} = \dfrac{{2 \times 11}}{{11}}\]
\[ \Rightarrow - 1 \times k = 2\]
Now, multiply both sides of the equation with \[ - 1\] as shown below.
\[ \Rightarrow - 1 \times - 1 \times k = - 1 \times 2\]
We know that multiplication of negative number to negative number is positive number and negative number with positive number is negative number.
\[\therefore 1 \times k = - 2\]
\[ \Rightarrow k = - 2\]
Thus, the solution for the given equation is \[k = - 2\].

Note: Product of two negative numbers or product of two positive numbers always gives a positive number and product of positive number with negative number gives a negative number.