Question

How do you solve $12=-3\left( 2-2r \right)-\left( 2r+2 \right)$ using distributive property?

Answer 1

Hint: We will first simplify the given equation using distributive property. We know that $a\left( b\pm c \right)=ab\pm ac$ hence using this we will open the brackets in the equation. Now we will separate the variable and constant terms and then simplify the equation to write it in the form of ar = b. Now we will divide the equation with a which is nothing but the coefficient of the variable in the equation. Hence we get the required value of r.

Complete step by step solution:
Now consider the given equation $12=-3\left( 2-2r \right)-\left( 2r+2 \right)$
The given equation is a linear equation in r.
Now we know that according to distributive property we have $a\left( b-c \right)=ab-ac$ and $a\left( b+c \right)=ab+ac$ .
Hence using distributive property we can say that $-3\left( 2-2r \right)=-3\left( 2 \right)-3\left( -2r \right)$ and $-1\left( 2r+2 \right)=\left( -1 \right)\left( 2r \right)+\left( -1 \right)\left( 2 \right)$
Hence using this in the given equation we get,
$\Rightarrow 12=-3\left( 2 \right)-3\left( -2r \right)-1\left( 2r \right)-1\left( 2 \right)$
Now on simplifying the above equation we get,
$\Rightarrow 12=-6+6r-2r-2$
Now we want to solve the equation and find the value of r. Hence let us first separate the constant terms and variable terms in the equation. Hence we get,
$\Rightarrow 12+6+2=6r-2r$
$\Rightarrow 20=4r$
Now we will divide the whole equation by coefficient of r. the coefficient of r is 4 hence on dividing the whole equation by 4 we get
$\Rightarrow r=5$
Hence the solution of the given equation is r = 5.

Note:
Now note that when we solve any equations we get the value of the variables in the equation. To check if the solution is correct, always substitute the obtained values of variables in the given equation, then we must get LHS = RHS. Hence if the equation holds the solution is correct.