Question

How do you solve $ 7\left( {2 + x} \right) = 35 $ using the distributive property?

Answer 1

Hint: In order to determine the value of variable $ x $ in the above equation, use the distributive property $ A\left( {B + C} \right) = AB + AC $ on LHS part to resolve parenthesis and simplify the equation. Now use the rules of transposing terms to transpose terms having $ (x) $ on the Left-hand side and constant value terms on the Right-Hand side of the equation. Combine and solve like terms and divide both sides of the equation with a coefficient of $ x $ get your required result.

Complete step-by-step answer:
 We are given a linear equation in one variable $ 7\left( {2 + x} \right) = 35 $ .and we have to solve this equation for variable ( $ x $ ).
 $ \Rightarrow 7\left( {2 + x} \right) = 35 $
Applying distributive law of multiplication on left-side of the equation to resolve the parenthesis and expand the terms as $ A\left( {B + C} \right) = AB + AC $
 $ \Rightarrow 7\left( 2 \right) + 7\left( x \right) = 35 $
Simplifying the equation, we get
 $ \Rightarrow 14 + 7x = 35 $
Now combining like terms on both of the sides. Terms having $ x $ 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 .In our case, $ 14 $ on the left-hand side will become $ - 14 $ on the right hand side .
After transposing terms our equation becomes
 $
   \Rightarrow 7x = 35 - 14 \\
   \Rightarrow 7x = 35 - 14 \\
   \Rightarrow 7x = 21 \;
  $
Dividing both sides of the equation with the coefficient of the variable $ x $ i.e. 7
 $
   \Rightarrow \dfrac{{7x}}{7} = \dfrac{{21}}{7} \\
   \Rightarrow x = 3 \;
  $
Therefore, the solution to the given equation is equal to $ x = 3 $ .
So, the correct answer is “ $ x = 3 $ ”.

Note: Linear Equation: 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 $ x $ which is the solution to the equation and if we put this $ x $ in the equation, the equation will be zero.