Question

How do you solve $12-2\left( x-5 \right)=20$ ?

Answer 1

Hint: Now in the equation we will first open the bracket. To open the bracket we will use distributive property which states $a\left( b-c \right)=ab-ac$ . Now we will separate variables and constants and simplify. Now we will find the value of x by dividing the equation by coefficient of x. Hence we get the solution of the given equation.

Complete step by step solution:
Now we are given with the equation $12-2\left( x-5 \right)=20$ .
Now we know that the given equation in a linear equation in one variable which is x.
To find the value of x we will first try to write the equation in the form of $ax=b$ .
Now first let us open the bracket of the equation by using the Distributive property.
We know by distributive property that for any real numbers a, b and c we have $a\left( b-c \right)=ab-ac$ . hence using this we get,
$\begin{align}
  & \Rightarrow 12-2\left( x \right)-2\left( -5 \right)=20 \\
 & \Rightarrow 12-2x+10=20 \\
\end{align}$
Now we will separate the variables and three constants in the equation hence we will shift 20 on LHS and 2x on RHS. Hence we get,
$\begin{align}
  & \Rightarrow 12+10-20=2x \\
 & \Rightarrow 2=2x \\
\end{align}$
Now we have the equation in the form $ax=b$ where a = 2.
Now dividing the whole equation by a which is 2 we get,
$\Rightarrow x=1$
Hence the value of x is 1.
Hence the solution of the given equation is x = 1.

Note:
Now note that while simplifying the equation with variables we can add terms which have the same variable with the same degree. Hence we can add 7x and 5x but not 7x and 5y or $7{{x}^{2}}$ and 5x.
This can be explained again by distributive property as we have $7x+5x=\left( 7+5 \right)x=12x$ .