Question

How do you solve \[3=7\left( 4-2u \right)-6u\]?

Answer 1

Hint: We will use the distributive property to simplify the equation, the distributive property is \[a\left( b+c \right)=ab+ac\]. As the highest power is one, the equation is linear in one variable. We know the standard procedure to solve these types of equations. The given equation has only a constant term on its left side. We need to flip the sides of the equation to get variable terms on the left side. We can do this either before solving the equation or at the end.

Complete step by step solution:
We are given the equation \[3=7\left( 4-2u \right)-6u\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[3=7\left( 4-2u \right)-6u\]
Using the distributive property to simplify the right-hand side of the above equation, we get
\[\Rightarrow 3=28-14u-6u\]
Subtracting 28 from both sides of the above equation, we get
\[\begin{align}
  & \Rightarrow 3-28=-20u \\
 & \Rightarrow -25=-20u \\
\end{align}\]
Flipping the above equation, we get
\[\begin{align}
  & \Rightarrow -20u=-25 \\
 & \Rightarrow \dfrac{-20u}{-20}=\dfrac{-25}{-20}=\dfrac{5}{4} \\
 & \therefore u=\dfrac{5}{4} \\
\end{align}\]
Hence, the solution of the above equation is \[u=\dfrac{5}{4}\].

Note: We can also solve the problem without using the distributive property as follows,
The given equation is \[3=7\left( 4-2u \right)-6u\]. Dividing by 7 to both sides of above equation, we get
\[\begin{align}
  & \Rightarrow \dfrac{3}{7}=\dfrac{7\left( 4-2u \right)-6u}{7} \\
 & \Rightarrow \dfrac{3}{7}=-\dfrac{6u}{7}+4-2u \\
\end{align}\]
Subtracting 4 from both sides, we get
\[\begin{align}
  & \Rightarrow \dfrac{3}{7}-4=-\dfrac{20u}{7} \\
 & \Rightarrow \dfrac{-25}{7}=-\dfrac{20u}{7} \\
\end{align}\]
Solving the above equation, we get \[u=\dfrac{5}{4}\].
Hence, we get the same answer from both methods.