Question

How do you solve $ - 7\left( {2b - 4} \right) = 5\left( { - 2b + 6} \right) $ ?

Answer 1

Hint: In order to determine the value of variable $ b $ in the above equation, use the distributive law of multiplication $ A\left( {B + C} \right) = AB + AC $ to resolve parenthesis. Use the rules of transposing terms to transpose terms having $ b $ on the left-hand side and constant value terms on the right-Hand side of the equation. Combine and solve like terms and divide the equation with coefficient of $ b $ to get your desired solution.

Complete step-by-step answer:
 We are given a linear equation in one variable $ - 7\left( {2b - 4} \right) = 5\left( { - 2b + 6} \right) $ .and we have to solve this equation for variable ( $ b $ ).
 $ - 7\left( {2b - 4} \right) = 5\left( { - 2b + 6} \right) $
Applying distributive law of multiplication on both sides terms to resolve the parenthesis and expand the term as $ A\left( {B + C} \right) = AB + AC $
 $ - 7\left( {2b} \right) - 7\left( { - 4} \right) = 5\left( { - 2b} \right) + 5\left( 6 \right) $
Simplifying the terms, we get
 $ - 14b + 28 = - 10b + 30 $
Now combining like terms on both of the sides. Terms having $ b $ will on the left-Hand side of the equation and constant terms on the right-hand side.
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term gets reversed .
After transposing terms our equation becomes
 $ - 14b + 10b = 30 - 28 $
Solving all the like term by resolving the operators,
 $ - 4b = 2 $
Dividing both sides of the equation with the coefficient of $ b $ i.e. $ - 4 $ , we obtain the value of $ b $ as
 $
\Rightarrow \dfrac{{ - 4b}}{{ - 4}} = \dfrac{2}{{ - 4}} \\
  b = - \dfrac{1}{2} \;
  $
Therefore, the solution to the given equation is equal to $ b = - \dfrac{1}{2} $
So, the correct answer is “ $ b = - \dfrac{1}{2} $ ”.

Note: 1. One must be careful while calculating the answer as calculation error may come.
2.There is only one value of $ b $ which is the solution to the equation and if we put this $ b $ in the equation, the equation will be zero.
3.Like terms are the terms who have the same variable and power.
Linear Equation in one variable: A linear equation is a equation which can be represented in the form of $ ax + c $ where $ x $ is the unknown variable and a,c are the numbers known where $ a \ne 0 $ .If $ a = 0 $ then the equation will become constant value and will no more be a linear equation .
The degree of the variable in the linear equation is of the order 1.
Every Linear equation has 1 root.