Question

How do you solve the equation \[-2r+6\left( r-1 \right)+3r-\left( 4-r \right)=-\left( r+5 \right)\]?

Answer 1

Hint: In order to find the solution of the given question that is to find how to solve \[-2r+6\left( r-1 \right)+3r-\left( 4-r \right)=-\left( r+5 \right)\] and find the value of \[r\], apply one of the properties of addition and multiplication that is associative property to simplify the expression and then take the terms with variable on one and other terms on the right side to get the value of variable \[r\].

Complete step by step solution:
According to the question, given equation in the question is as follows:
\[-2r+6\left( r-1 \right)+3r-\left( 4-r \right)=-\left( r+5 \right)\]
To solve the above equation, simplify the terms on the left-hand side of the equation by opening the brackets with the help of associative property, we will have:
\[\Rightarrow -2r+6r-6+3r-4+r=-\left( r+5 \right)\]
Then simplify the terms on the left-hand side of the equation by using addition, we will have:
\[\Rightarrow 8r-10=-\left( r+5 \right)\]
After simplifying the above equation by solving the bracket on the right-hand side of the equation, we will have:
\[\Rightarrow 8r-10=-r-5\]
Now add the term \[5\] on both the sides, we will have:
\[\Rightarrow 8r-10+5=-r-5+5\]
After simplifying the above equation with the help of addition, we will have:
\[\Rightarrow 8r-5=-r\]
Now take all the like terms like one with variable \[r\] to left-hand side of the above equation and rest to the right-hand side, we will have:
\[\Rightarrow 8r+r=5\]
After solving the terms in the left-hand side of the above equation with the help of addition, we will have:
\[\Rightarrow 9r=5\]
Now divide \[9\] to both the sides of the above equation, we will have:
\[\Rightarrow \dfrac{9r}{9}=\dfrac{5}{9}\]
After simplifying the above equation with the help of division, we will have:
\[\Rightarrow r=\dfrac{5}{9}\]
Therefore, after solving the equation \[-2r+6\left( r-1 \right)+3r-\left( 4-r \right)=-\left( r+5 \right)\], the value of variable \[r\] is \[\dfrac{5}{9}\].

Note: Students make mistakes in miscalculations while opening the bracket and not multiplying the sign of the term which is completely wrong and leads to the wrong answer. It’s important to cross check the answer again once solved to avoid such miscalculations while solving the brackets in this type of question.