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How do you solve for x in \[ax - k = bx + h\] ?

Last updated date: 03rd Mar 2024
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IVSAT 2024
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Hint:In this question, an algebraic expression containing five unknown variable quantities is given to us. We know that we need an “n” number of equations to find the value of “n” unknown variables. So to find the value of each unknown variable we need 5 equations, but in the given question, we have to solve for x. So, we treat the other unknown variables as constant, now we have 1 unknown quantity and exactly one equation to find the value of x. For finding the value, we will rearrange the equation such that x lies on 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 \[ax - k = bx + h\]
To find the value of x, we will take $bx$ to the left-hand side and k to the right-hand side so that the terms containing x are present on one side and the constant terms are present on the other side –
$ \Rightarrow ax - bx = h + k$
Taking x common –
$x(a - b) = h + k$
Now, we will take $(a - b)$ to the right-hand side –
$x = \dfrac{{h + k}}{{a - b}}$
Hence, when \[ax - k = bx + h\] , we get $x = \dfrac{{h + k}}{{a - b}}$ .

Note: The obtained equation contains x on the one side and the terms a, b, h and k on the other side, so we can get the value of x by putting the values of a, b, h and k in the obtained equation. The answer is in fractional form, so after putting the values of a, b, h and k, we will also simplify the fraction, if it is not in the simplified form.
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