Question

How do you solve $3\left( {2w + 8} \right) = 60$?

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 addition is given by:
$a\left( {b + c} \right) = a \cdot b + a \cdot c$

Complete step by step solution:
We are given the expression $3\left( {2w + 8} \right) = 60$. First, apply the distributive property of multiplication over the addition to the left hand side of the expression.
$ \Rightarrow 3 \cdot 2w + 3 \cdot 8 = 60$
On simplifying the equation, we get:
$ \Rightarrow 6w + 24 = 60$
Now, we will subtract $24$from both sides of the equation.
$ \Rightarrow 6w + 24 - 24 = 60 - 24$
$ \Rightarrow 6w = 36$
Now, divide both sides of the equation by $6$.
$ \Rightarrow \dfrac{{6w}}{6} = \dfrac{{36}}{6}$
$ \Rightarrow w = 6$
Hence, the solution of the expression is equal to $w = 6$.

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: The students must note that we have used the distributive property in the solution. Distributive Property: If we have any 3 numbers a, b and c, then we have:
$a\left( {b + c} \right) = a \cdot b + a \cdot c$
Here, we just replaced a, b and c by the required numbers and thus obtained the expressions as we did in the solution above.
The students must note that they may also use the same property without taking two different variables x and y and just solving everything in the same line.