Question

How do you simplify $10+4\left( x+1 \right)+5$ ?

Answer 1

Hint: Problems of this type can be easily solved by using distributive property of numbers. The distributive property tells us how to solve expressions in the form of $a\left( b+c \right)$ . We first simplify each of the terms by applying the distributive property of numbers by opening the first bracket and multiplying the terms by $4$ , then adding all the like terms we reach to the simplified form.

Complete step by step answer:
For simplifying this type of mathematical equations, the first step will be simplifying each of the terms as much as possible. First, we will approach the complicated terms in the equation.
As in this case the middle term $4\left( x+1 \right)$ must be taken care of at first. We must apply the distributive property of numbers which is also known as the Distributive Law.
According to the distributive law any term expressed as $a\left( b+c \right)$ can be simplified by multiplying the number outside the bracket (which is $a$ here) with each of the numbers inside the bracket (which are $b$ and $c$ here) and adding them at last. Hence, it will become $ab+ac$ .
We take the term $4\left( x+1 \right)$and Distribute. That is multiply each term in the bracket by $4$ .
Hence, $4x+4\cdot 1=4x+4$
 The expression is now: $10+4x+4+5$
 Now collecting the 'like terms" gives
\[4x+10+\text{ }4+5=4x+19\]

Therefore, we can conclude that the given expression in the question can be simplified to $4x+19$.

Note: For simplifying equations of this type, we must strictly follow the BODMAS priority rule (Priority order as follows: Bracket, Order, Division, Multiplication, Addition, and Subtraction). Also, the distributive property must be applied carefully to avoid mistakes.