Question

How do you solve \[\dfrac{{b + 1}}{3} = 2\]?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation as there is a constant variable involved and to solve this expression, combine all the like terms and then simplify the terms to get the value of b.

Complete step by step solution:
Let us write the given expression,
\[\dfrac{{b + 1}}{3} = 2\]
Multiplying both sides by 3 to the given expression, we get:
\[ \Rightarrow 3 \cdot \dfrac{{b + 1}}{3} = 2 \cdot 3\]
As, the numerator and denominator consist of same terms, we get:
\[ \Rightarrow b + 1 = 6\]
Subtracting 1 from both sides of the obtained equation, we have:
\[ \Rightarrow b + 1 - 1 = 6 - 1\]
Simplifying the common terms, we get:
\[ \Rightarrow b = 6 - 1\]
\[ \Rightarrow b = 5\]

Additional information:
Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.
Solving simultaneous equations by Substitution: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Note: The key point to solve this type of equation is to combine all the like terms and evaluate for the variable asked. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved. As we know that Simultaneous equations are two equations, each with the same two unknowns and are "simultaneous" because they are solved together.