Question

How do you solve the linear equation \[\dfrac{2}{3}x+1=-5\]?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will find out the value of x. In solving this question, we will first put all the constant terms to the right side of the equation and variable terms to the left side of the equation. After that, we will do the cross-multiplication. After solving the further equation, we will get the value of x.

Complete step by step solution:
Let us solve this question.
In this question, we will solve the given equation and find out the value of x. The given equation is \[\dfrac{2}{3}x+1=-5\].
The equation which we have to solve is
\[\dfrac{2}{3}x+1=-5\]
Let us take the constant term 1 from the left side of the equation to the right side of the equation. we can write the above equation as
\[\Rightarrow \dfrac{2}{3}x=-5-1\]
The above equation can also be written as
\[\Rightarrow \dfrac{2}{3}x=-6\]
\[\Rightarrow \dfrac{2x}{3}=-6\]
Now, doing the cross-multiplication, we can write
\[\Rightarrow 2x=-6\times 3\]
The above equation can also be written as
\[\Rightarrow 2x=-18\]
Now, dividing 2 to both the side of the equation, we get
\[\Rightarrow \dfrac{2x}{2}=\dfrac{-18}{2}\]
The above can also be written as
\[\Rightarrow x=-9\]
Hence, we have solved the equation \[\dfrac{2}{3}x+1=-5\] and found the value of x as -9.

Note: We should have a better knowledge in the topic of algebra. we should know about cross-multiplication. Let us understand this from the following:
\[\dfrac{a}{b}=\dfrac{c}{d}\]
The above can also be written according to cross-multiplication as
\[a\times d=b\times c\]
We can check if our answer is correct or not by putting the value of x in the given equation.
So, let us put the value of x as -6 in the equation \[\dfrac{2}{3}x+1=-5\], we can write
\[\dfrac{2}{3}\left( -9 \right)+1=-5\]
The above can also be written as
\[\Rightarrow 2\left( -3 \right)+1=-5\]
The above equation can also be written as
\[\Rightarrow -6+1=-5\]
\[\Rightarrow -5=-5\]
Hence, we get that both sides of the equation are equal. So, our answer is correct.