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Solve the following equation:
 4(2x – 1) – 2(x – 5) = 5(x + 1) + 3

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: In this particular type of question we firstly have to simplify the given equation by using the BODMAS method. After simplification, reorder the terms, combine like terms and solve for variable 'x' to get the desired answer.

Complete step by step answer:
So, let us apply the BODMAS Rule in the given equation.
Now as we know that according to the BODMAS Rule. We had to first solve the brackets.
So, first solving the brackets of the given equation.
\[ \Rightarrow \]4(2x – 1) – 2(x – 5) = 5(x + 1) + 3
As the terms inside the brackets are already solved because we cannot add or subtract constant terms. So, now we can open all the brackets in the above equation.
\[ \Rightarrow \]8x – 4 – 2x + 10 = 5x + 5 + 3
Now only addition and subtraction signs are left in the above equation. So, solving the above equation.
\[ \Rightarrow \]8x – 2x + 6 = 5x + 8
\[ \Rightarrow \]6x + 6 = 5x + 8
Now LHS and RHS of the above equation are simplified. So, now we had to take all the terms with x to the one side of the equation and all the constant terms to another side of the equation to find the value of x.
So, subtracting 5x from both the sides of the above equation.
\[ \Rightarrow \]6x – 5x + 6 = 8
\[ \Rightarrow \]x + 6 = 8
Now subtracting 6 form both the sides of the above equation.
\[ \Rightarrow \]x = 8 – 6 = 2

Hence, x = 2

Note: Whenever we face such types of problems, we should order and combine the terms properly. Also, we should remember the BODMAS method which is Bracket Of Division, Multiplication, Addition and Subtraction which tells the order to solve such kinds of questions. So, first, we had to solve the brackets and then if there is “of” present in the equation then solve that, after that do division, multiplication, addition and subtraction. On solving these equations without the BODMAS order we will get the incorrect answer. So, after solving LHS and RHS we can take constant terms to one side of the equation and variable to the other side of the equation to find the value of the variable. This will be the easiest and efficient way to find the solution of the problem.
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