Let's look at the given equation.

7 (x + 5) - x = 42

When we simplify an expression with different types of operations, we always need to remember the order of operations. The acronym PEMDAS can help with that!

First we simplify calculations that are in

parentheses .

Second, we calculate

exponents

and

roots .

Then, we simplify

multiplication

and

division,

which are solved on the same level of importance and from left to right. Finally, we calculate

addition

and

subtraction,

which are also on the same level of importance, from left to right. Let's now again look at our expression.

7 (x + 5) - x = 42

According to the order of operations, we need to start by removing the

parentheses .

We can do it using Distributive Property.

Now our expression contains only multiplication, addition, and subtraction.

7 \cdot x + 7 \cdot 5 - x = 42

This mean that we should start with multiplication.

7 x + 35 - x = 42

After the multiplication, we have two like terms,

7 x

and

- x .

Let's combine them!

7 x + 35 - x = 42

SubTerm

Subtract term

6 x + 35 = 42

Without Distributive Property

We will now try to start by combining like terms before using the Distributive Property.

7 (x + 5) - x = 42

SubTerm

Subtract term

7 (5) = ? 42

Multiply

35 \neq = 42 \times

This attempt resulted in contradiction. According to the order of operations, we need to start by removing the parentheses. We cannot remove

x

from the inside of the parentheses, without multiplying it by

7 .

In the given expression, the correct like terms are

7 x

and

- x,

but it is only easy to see after applying the Distributive Property.

Exercise