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How do you solve for x in $5x + 3 > 2x - 9$ ?

Last updated date: 26th Feb 2024
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IVSAT 2024
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Hint:In this question, we are given that \[5x + 3\] is greater than $2x - 9$ , it is an algebraic expression containing one unknown variable quantity (x). We know that we need an “n” number of equations to find the value of “n” unknown variables. In the given algebraic expression; we have exactly one equation and 1 unknown quantity, so we can easily find the value of x by rearranging the equation such that one side of the equation contains the terms containing x 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 $5x + 3 > 2x - 9$
To find the value of x, we will take 2x to the left-hand side and 3 to the right-hand side –
5x - 2x > - 9 - 3 \\
\Rightarrow 3x > - 12 \\
Now, we will take 3 to the right-hand side –
$x > \dfrac{{ - 12}}{3}$
The answer obtained is a fraction, now we have to simplify this fraction by prime factorization of the numerator and the denominator –
$x > \dfrac{{ - 2 \times 2 \times 3}}{3}$
3 is present in both the numerator and the denominator, so we cancel them out –
$ \Rightarrow x > - 4$
Hence, when $5x + 3 > 2x - 9$ , we get $x > - 4$ .

Note: In the given algebraic expression, the alphabet representing the unknown quantity has a non- negative integer as power, that is, 1. So the given expression is a polynomial equation and is known as a linear equation as the degree of x is 1 (degree is defined as the highest power of the unknown quantity in a polynomial equation).
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