Question

How do you solve $ 2-4a=16 $ ?

Answer 1

Hint: In the problem, we need to solve the equation $ 2-4a=16 $ . The solution of the above equation means calculating the value of $ a $ which satisfies the above-given equation. We can observe that arithmetic operations like addition and multiplication are present in the given equation. To solve the given equation, we need to apply the reverse arithmetic operations for the equation. We know that subtraction is the reverse arithmetic operator for addition and division is the reverse arithmetic operator for multiplication. So, we will first perform subtraction followed by division and simplify the obtained equation to get the required result.

Complete step by step answer:
Given that, $ 2-4a=16 $
We can observe that $ 2 $ is in addition on the left-hand side of the above equation. To solve the equation, we need to perform subtraction operations on both sides.
Subtracting $ 2 $ on both sides of the above equation, then we will get
 $ 2-4a-2=16-2 $
We know that $ +a-a=0 $ , applying this value in the above equation and simplifying, then we will get
 $ \Rightarrow -4a=14 $
Multiplying the negative sign on both sides of the above equation, then we will have
 $ \Rightarrow -\left( -4a \right)=-14 $
We know that when we multiply a negative sign with a negative sign then we will get a positive sign. Then the above equation is modified as
 $ \Rightarrow 4a=-14 $
We can observe that $ 4 $ is in multiplication in the above equation. To solve the above equation, we need to divide the whole equation with $ 4 $ . Then the above equation will be
 $ \Rightarrow \dfrac{4a}{4}=\dfrac{-14}{4} $
Simplifying the above equation, then we will get
 $ \therefore a=-\dfrac{7}{2} $.

Note:
We can check whether the calculated solution is right or wrong by substituting the calculated $ a $ value in the given equation.
Given $ 2-4a=16 $ .
Calculated $ a $ value is $ a=-\dfrac{7}{2} $ . Substituting this value in the given equation, then we will get
 $ 2-4\left( \dfrac{-7}{2} \right)=16 $
Simplifying the above equation, then we will get
 $ \begin{align}
  & \Rightarrow 2-2\left( -7 \right)=16 \\
 & \Rightarrow 2+14=16 \\
 & \Rightarrow 16=16 \\
 & \Rightarrow LHS=RHS \\
\end{align} $
Hence the calculated solution is correct.