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How do you solve for x in the equation $a = bx + c$ ?

Last updated date: 20th Jun 2024
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Hint:In this question, we are given an algebraic expression containing one unknown variable quantity. 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 1 unknown quantity and exactly one equation to find the value of x.
For that, we will rearrange the equation such that x lies 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 $a = bx + c$
To find the value of x, we will take c to the left-hand side or we can subtract c from both the sides –
$ \Rightarrow a - c = bx$
Now, we will take b to the left-hand side or we can divide both the sides by b –
$\dfrac{{a - c}}{b} = x$
Hence, when $a = bx + c$ , we get $x = \dfrac{1}{b}(a - c)$

Note: Algebraic expressions are known as the mathematical equations that are a combination of numerical values and alphabets. The alphabets represent some unknown quantities, the alphabets and numerical values are linked via arithmetic operations like addition, subtraction, multiplication and division. The obtained equation contains x on the one side and the terms a, b and c 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.