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 * x + 7 * 5 -x=42
This mean that we should start with multiplication.
7x + 35 - x=42
After the multiplication, we have two like terms, 7x and - x. Let's combine them!
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 7x and - x, but it is only easy to see after applying the Distributive Property.
