Question

Solve and check \[3x+2(x+2)=20-(2x-5)\]

Answer 1

Hint: In this type of question we need to first evaluate the equation by simplifying the equations on both sides and keeping the variable on one side, we need to check whether the value of the variable we calculated should give the same result on both sides of the original equation.

Complete step-by-step answer:
To solve such type equations we need to find out the terms with variables present in it by solving it algebraically. We need to keep in mind that when a positive term is transferred from one side to another side of the equation it becomes negative. Similarly when a negative term is transferred from one side to another side of the equation it becomes positive. Similarly when it is divided it becomes multiplication when transferred from one side to another side of the equation and vice versa for the multiplication.
Given that \[3x+2(x+2)=20-(2x-5)\]
On opening brackets on both the sides
 \[\Rightarrow 3x+2(x)+2(2)=20-2x-(-5)\]
Now simplifying further,
 \[\Rightarrow 3x+2x+4=20-2x+5\]
 \[\Rightarrow 5x+4=25-2x\]
Now take all the terms containing \[x\] on one side.
We get the equation as:
 \[\Rightarrow 5x+2x=25-4\]
On solving the equation, we get:
 \[\Rightarrow 7x=21\]
So, \[x=\dfrac{21}{7}\]
The value of \[x\] obtained is \[x=3\]
Now, check the given equation.
For checking we have to substitute the value \[x=3\] in the given equation on both sides .If the Left hand side expression and Right hand side of expression becomes equal then the given equation is right. But if the Left hand side expression and Right hand side of expression is not the same then the given equation is wrong.
Now, substituting \[x=3\] in left hand side expression:
LHS-
 \[3x+2(x+2)\]
 \[\Rightarrow 3(3)+2(3+2)\]
On solving:
 \[\begin{align}
  & \Rightarrow 9+2(5) \\
 & \Rightarrow 9+10 \\
 & \Rightarrow 19 \\
\end{align}\]
The value of left hand side expression after substituting the value of \[x\] is \[19\] .
Now, substituting \[x=3\] in right hand side expression:
RHS-
 \[20-(2x-5)\]
 \[\Rightarrow 20-(2(3)-5)\]
On Solving:
 \[\begin{align}
  & \Rightarrow 20-(6-5) \\
 & \Rightarrow 20-1 \\
 & \Rightarrow 19 \\
\end{align}\]
The value of right hand side expression after substituting the value of \[x\] is \[19\] .
Since, the value after substituting \[x\] on left hand side expression and right hand side expression is same, i.e.
 \[LHS=RHS\]
Hence, the given equation is right.
The value of \[x\] obtained is \[3\] and the given equation is correct.
So, the correct answer is “x = 3”.

Note: Linear equations are applicable in day to day life, for example as computers use linear equations for weather forecasting models, we can predict profit or loss by using graphs of equations. These basically allow scientists to describe the relationship between variables in a physical world.