Question

How do you solve for $b$ in $ab + c = d$?

Answer 1

Hint: First step is to isolate $ab$ term on one side by performing the same mathematical operations on both sides of the equation. So, subtract $c$ from both sides of the given equation. Next step is to make the coefficient of $b$ equal to $1$ using multiplication or division property. So, divide each term by $a$ and simplify.

Complete step-by-step solution:
Given equation is $ab + c = d$.
We have to find the value of $b$.
First step is to isolate $ab$ term on one side by performing the same mathematical operations on both sides of the equation.
So, subtracting $c$ from both sides of the given equation.
$ \Rightarrow ab + c - c = d - c$
It can be written as
$ \Rightarrow ab = d - c$
Next step is to make the coefficient of $b$ equal to $1$ using multiplication or division property.
So, dividing each term by $a$ and simplifying.
Divide each term in $ab = d - c$ by $a$.
$ \Rightarrow \dfrac{{ab}}{a} = \dfrac{{d - c}}{a}$
Separate the denominator in RHS.
$ \Rightarrow \dfrac{{ab}}{a} = \dfrac{d}{a} + \dfrac{{ - c}}{a}$
Now, cancel the common factor of $a$.
Cancel the common factor.
$ \Rightarrow \dfrac{{\not{a}b}}{{\not{a}}} = \dfrac{d}{a} + \dfrac{{ - c}}{a}$
Divide $b$ by $1$.
$ \Rightarrow b = \dfrac{d}{a} + \dfrac{{ - c}}{a}$
Now, move the negative in front of the fraction.
$\therefore b = \dfrac{d}{a} - \dfrac{c}{a}$

Therefore, $b = \dfrac{d}{a} - \dfrac{c}{a}$.

Note: An algebraic equation is an equation involving variables. It has an equality sign. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).
In an equation the values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.