Question

How do you solve $0 > 9\left( k-\dfrac{2}{3} \right)+33$?

Answer 1

Hint: The given equation is inequality equation. To solve the given equation first we will multiply the terms inside the bracket on the right side by 9. Then we simplify the equation obtained on the right side by solving the operators given. Then by simplifying the obtained equation we get the value of k.

Complete step by step solution:
We have been given an equation $0>9\left( k-\dfrac{2}{3} \right)+33$.
We have to solve the given equation and find the value of k.
Now, to solve the given inequality first we will solve the bracket given at the right side. For this we multiply the terms inside the bracket by 9. Then we will get
$\Rightarrow 0>9k-9\times \dfrac{2}{3}+33$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 0>9k-6+33 \\
 & \Rightarrow 0>9k+27 \\
\end{align}$
Now, dividing the whole equation by 9 we will get
$\Rightarrow 0>\dfrac{9k}{9}+\dfrac{27}{9}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 0>k+3 \\
 & \Rightarrow -3>k \\
 & \Rightarrow k<-3 \\
\end{align}$

It means any value less than $-3$ satisfies the given equation.

Note: Inequalities are mathematical expressions which can be solved by using algebra or by drawing graphs. The fact about the inequality is that if we multiply or divide both sides of the inequality by a negative number then the inequality no longer remains true, the inequality becomes reverse. We can multiply or divide each side by the same positive number. In fact we can add and subtract by any number at each side. The point to be remembered is that we cannot replace the inequality sign by equal sign.