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Last updated date: 13th Jun 2024
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Answer
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Hint: The given expression is an equation. Here, the ‘ $=$ ‘ sign is used to show that the left-hand side is equal to the right-hand side for some value of $b$ . So, to solve the equation, we have to find the value of the variable which is represented as $b$ .

Complete step by step answer:
We need to solve the given equation,
$- 11b + 7 = 40$
First of all, the above expression is called an equation, because in it the equal sign ‘ $=$ ‘ is used, which shows that the two expressions are equal.
In an equation, there is a left-hand side, an equal sign ‘ $=$ ‘, and a right-hand side.
Also, the given equation contains a variable, whose value is to be determined to solve the given equation.
Consider the equation,
$- 11b + 7 = 40$
To solve the above equation, we first subtract $7$ on both sides,
$\Rightarrow - 11b + 7 - 7 = 40 - 7$
$\Rightarrow - 11b = 33$
Now, dividing both sides by the coefficient of $b$ which is $- 11$ , we get
$\Rightarrow \dfrac{{ - 11b}}{{ - 11}} = \dfrac{{33}}{{ - 11}}$
$\Rightarrow b = - 3$ .

Thus, we can say that for the equation $- 11b + 7 = 40$ , the solution is $b = - 3$ .

Note: In the given equation, the variable is $b$ . The equation $- 11b + 7 = 40$ also contains a constant, which is a value that does not change. $- 11$ is the coefficient of $b$ .
In Algebra, we use letters to represent unknown numbers. This way it becomes easier to solve the problems and to obtain the value of unknown numbers. The unknown number that is represented by a letter is called the variable. Variable is a letter that is used to indicate a value that varies.