Question

How do you solve $9\left( {4b - 1} \right) = 2\left( {9b + 3} \right)$?

Answer 1

Hint: Given an expression. We have to find the value of the expression using the distributive property of multiplication over the subtraction. The terms outside the parentheses are multiplied with every other term inside the parentheses. Then, simplify the expression by subtracting the terms and write the simplified expression.

Formula used:
The distributive property of multiplication over the subtraction is given by:
$a\left( {b - c} \right) = a \cdot b - a \cdot c$

Complete step by step solution:
We are given the expression $9\left( {4b - 1} \right) = 2\left( {9b + 3} \right)$. First, apply the distributive property of multiplication to both sides of the expression.
$ \Rightarrow 9 \cdot \left( {4b} \right) + 9\left( { - 1} \right) = 2 \cdot \left( {9b} \right) + 2\left( 3 \right)$
On simplifying the equation, we get:
$ \Rightarrow 36b - 9 = 18b + 6$
Now, we will add 9 to both sides of the equation.
$ \Rightarrow 36b - 9 + 9 = 18b + 6 + 9$
$ \Rightarrow 36b = 18b + 15$
Subtract $18b$ from both sides of equation, we get:
$ \Rightarrow 36b - 18b = 18b - 18b + 15$
$ \Rightarrow 18b = 15$
Divide both sides of the equation by $18$.
$ \Rightarrow \dfrac{{18b}}{{18}} = \dfrac{{15}}{{18}}$
$ \Rightarrow b = \dfrac{5}{6}$

Final answer: Hence, the solution of the expression is equal to $b = \dfrac{5}{6}$

Additional information:
In the algebraic expression which involves the parentheses. The terms in the parentheses, then multiply each term inside the parentheses with the term outside the parentheses, and this property is known as the distributive property of multiplication over the addition. Then, the expression is simplified until all the parentheses are removed. The multiplication of the terms is commutative. Then, the variables with like terms are combined with each other. To simplify the expression, check whether the terms are added or subtracted with each other or not.

Note:
In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students mainly forget to apply the correct operation on the equation such that the expression is simplified and the brackets are solved. Students may get confused while first multiplying each term and then subtract the like terms.