Question

How do you solve the equation \[20=14+3\left( x+8 \right)\]?

Answer 1

Hint: This question is from the topic of linear equations. The linear equation always has only one solution. We will find the value of x in this question. We will first multiply the term outside of the bracket with the term inside the bracket. After that, we will take all the terms of x to the left side of the equation and all the constants to the right side of the equation. After that, we will solve the equation and find the value of x.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to solve the equation \[20=14+3\left( x+8 \right)\]. We have to find the value of x from the given equation.
The given equation is
\[20=14+3\left( x+8 \right)\]
By multiplying the term outside the parenthesis or bracket that is 3 with the term inside the parenthesis or bracket that is (x-3), we will get
\[\Rightarrow 20=14+3x+3\times 8\]
As we know that 3 multiplied 8 is 24, so, we can write the above equation as
\[\Rightarrow 20=14+3x+24\]
Now, taking the term of x to the left side of equation, we can write the equation as
\[\Rightarrow -3x+20=14+24\]
Taking all the constant terms to the right side of the equation, we will get
\[\Rightarrow -3x=14+24-20\]
The above equation can also be written as
\[\Rightarrow -3x=38-20\]
The above equation can also be written as
\[\Rightarrow -3x=18\]
Now, dividing -3 to the both side of the equation, we get
\[\Rightarrow x=-6\]
Hence, we have solved the equation \[20=14+3\left( x+8 \right)\] and get the value of x as -6.

Note: We should know how to find the value of a variable from the given linear equation to solve this type of question. If we want to check if our answer is correct or not, then we can cross-check our answer by putting the value of the variable in the given equation.
The equation is
\[20=14+3\left( x+8 \right)\]
Now, putting the value of x as -6, we get
\[\Rightarrow 20=14+3\left( -6+8 \right)\]
The above equation can also be written as
\[\Rightarrow 20=14+3\left( 2 \right)\]
The above equation can also be written as
\[\Rightarrow 20=14+6\]
\[\Rightarrow 20=20\]
Hence, both sides of the equation get equal. So, we get that our answer is correct.