Question

How do you solve $ 7\left( {10 - 3w} \right) = 5\left( {15 - 4w} \right) $ ?

Answer 1

Hint: In order to determine the value of variable $ w $ 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 $ w $ on the left-hand side and constant value terms on the right-Hand side of the equation. Combine and solve like terms and multiply both sides of the equation with a coefficient of $ w $ to get your desired solution.

Complete step by step solution:
 We are given a linear equation in one variable
 $ 7\left( {10 - 3w} \right) = 5\left( {15 - 4w} \right) $ .and we have to solve this equation for variable ( $ w $ ).
 $ 7\left( {10 - 3w} \right) = 5\left( {15 - 4w} \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( {10} \right) + 7\left( { - 3w} \right) = 5\left( {15} \right) + 5\left( { - 4w} \right) $
Simplifying the terms, we get
 $ \Rightarrow 70 - 21w = 75 - 20w $
Now combining like terms on both of the sides. Terms having $ w $ 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
 $ - 21w + 20w = 75 - 70 $
Solving all the like term by resolving the operators,
 $ - w = 5 $
Multiplying both sides of the equation with the coefficient of $ w $ i.e. $ - 1 $ , we obtain the value of $ w $ as
 $
\Rightarrow - 1\left( { - w} \right) = - 1\left( 5 \right) \\
\Rightarrow w = - 5 \;
  $
Therefore, the solution to the given equation is equal to $ w = - 5 $
So, the correct answer is “ $ w = - 5 $ ”.

Note: 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.
1. One must be careful while calculating the answer as calculation error may come.
2.There is only one value of $ w $ which is the solution to the equation as it is a linear equation and if we put this $ w $ in the equation, the equation will be zero.