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# How do you solve for x in $ax + b = cx$ ?

Last updated date: 04th Aug 2024
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Hint:In this question, we are given an algebraic expression containing three unknown variable quantities. We know that to find the value of “n” unknown variables, we need “n” number of equations. That’s why we need 3 equations to find the value of each unknown variable, but in the given question, we have to solve for x. So, the other unknown variables are treated as constant, now we have exactly one equation and 1 unknown quantity 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.

We are given that $ax + b = cx$
To find the value of x, we will take $ax$ 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 –
$\Rightarrow b = cx - ax$
Taking x common –
$\Rightarrow b = x(c - a)$
Now, we will take $(c - a)$ to the left-hand side –
$x = \dfrac{b}{{c - a}}$
Hence, when $ax + b = cx$ , we get $x = \dfrac{b}{{c - a}}$ .

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