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How do you solve for x in $6x - 5 = 25$ ?

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Last updated date: 03rd Mar 2024
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IVSAT 2024
Answer
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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 $6x - 5 = 25$
To find the value of x, we will take 5 to the right-hand side –
$
6x = 25 + 5 \\
\Rightarrow 6x = 30 \\
$
Now, we will take 6 to the right-hand side –
$x = \dfrac{{30}}{6}$
The answer obtained is a fraction, now we have to simplify this fraction by prime factorization of the numerator and the denominator –
$x = \dfrac{{2 \times 3 \times 5}}{{2 \times 3}}$
2 and 3 are present in both the numerator and the denominator, so we cancel them out –
$ \Rightarrow x = 5$
Hence, when $6x - 5 = 25$ , we get $x = 5$ .

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 represents the value 5 which was obtained by solving the expression. The answer obtained is a fraction that is not in a simplified form so we simplify it by canceling out the common factors present in the numerator and the denominator.
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