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How do you solve for x in the equation \[\dfrac{{6x - 5}}{2} = 2x + 6\] ?

Last updated date: 17th Jun 2024
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Hint:In this question, we are given an algebraic expression containing one unknown variable quantity. We know that to find the value of “n” unknown variables, we need “n” number of equations. In the given algebraic expression, we have 1 unknown quantity and exactly one equation to find the value of x. So we can easily find the value of x by rearranging the equation such that the terms containing x lie on the one side of the equation and all other terms lie on the other side. Then by applying the given arithmetic operations, we can find the value of x.

Complete step by step answer:
We are given that \[\dfrac{{6x - 5}}{2} = 2x + 6\]
To find the value of x, we will take 2 to the right-hand side or we can multiply both the sides by 2 –
6x - 5 = 2(2x + 6) \\
\Rightarrow 6x - 5 = 4x + 12 \\
Now, we will take 4x to the left-hand side and 5 to the right-hand side –
6x - 4x = 12 + 5 \\
\Rightarrow 2x = 17 \\
Now, we will take 2 to the right-hand side –
$x = \dfrac{{17}}{2}$
Hence, when \[\dfrac{{6x - 5}}{2} = 2x + 6\] , we get $x = \dfrac{{17}}{2}$ .

Note: The mathematical equations that are a combination of numerical values and alphabets are known as algebraic expressions. The alphabets in the algebraic expression represent some unknown quantities, like in the question x represented the value $\dfrac{{17}}{2}$ which was obtained by solving the expression. The answer obtained is a fraction that is already in simplified form. If the fraction obtained is not in simplified form, then we would cancel out the common factors present in the numerator and the denominator.