Question

How do you solve \[-3\left( x-5 \right)<9\]?

Answer 1

Hint: This question is from the topic of algebra. In solving this question, we will first divide the term 3 to the both sides of the equation. After that, we will multiply -1 to the both sides of the equation. After that, we will take 5 to the right side of the equation. After solving the further equation, we will get the value of x. After that, we will see an alternate method to solve this question.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to solve the term \[-3\left( x-5 \right)<9\]. Or, we can say that we have to solve the equation \[-3\left( x-5 \right)<9\] and have to find the value of x.
The equation we have to solve is given as
\[-3\left( x-5 \right)<9\]
Let us divide the above equation on both sides by 3, we will get
\[\Rightarrow \dfrac{-3\left( x-5 \right)}{3}<\dfrac{9}{3}\]
The above equation can also be written as
\[\Rightarrow -\dfrac{3}{3}\left( x-5 \right)<\dfrac{9}{3}\]
As we know that 3 divided by 3 is 1 and 9 divided by 3 is 3, so we can write
\[\Rightarrow -\left( x-5 \right)<3\]
Now, by multiplying the negative inside the parenthesis we can write the above equation as
\[\Rightarrow -x+5<3\]
Now, we will take the constant 5 to the right side of the equation. So, the above equation can also be written as
\[\Rightarrow -x<3-5\]
We can write the above equation as
\[\Rightarrow -x<-2\]
Now, taking x to the right side of equation and 2 to the left side of equation, we get
\[\Rightarrow 2We can write the above equation as
\[\Rightarrow x>2\]
So, we have solved the question and found the value of x as greater than 2.

Note:
We should have a better knowledge in the topic of algebra to solve this type of question. Let us solve this question by an alternate method. The equation is
\[-3\left( x-5 \right)<9\]
After dividing 3 to both side of the equation, we get
\[\Rightarrow \dfrac{-3\left( x-5 \right)}{3}<\dfrac{9}{3}\]
The above equation can also be written as
\[\Rightarrow -\left( x-5 \right)<3\]
The above equation can also be written as
\[\Rightarrow -x+5<3\]
Remember that if we multiply negative terms to both sides of the equation, then sign of changes. If the sign is <, then it will change to > and if the sign is >, then it will change to <.
Let us multiply -1 to the both sides of the equation. So, we can write the above equation as
\[\Rightarrow -1\left( -x+5 \right)>-1\times 3\]
The above equation can also be written as
\[\Rightarrow x-5>-3\]
The above equation can also be written as
\[\Rightarrow x>-3+5\]
\[\Rightarrow x>2\]
So, we have got the same answer. Hence, we can use this method too to solve this question.