Question

Simplify the following expression and show your work in details please .

Answer 1

Answer:

$4m + 5 - 3m \\ = 4m - 3m + 5 \\ = 1m + 5 \\ = (m + 5)$

Answer 2

Given the expression:

$\displaystyle \large{4m + 5 - 3m}$

To simplify the expression, notice that 4m and 3m have the same term.

These are called like terms. Let's see some examples of like terms.

• x and 58x both are like terms because they have same x.
• 90y and 35664y both are also like terms because they have same y.

Then we also have the example of non-like term

• 50 and x both are not like terms because 50 is a constant and not a variable and x is not a number.
• 920x and 790y both are not like terms because both have different variables.
• x and x^2 are not like terms as well because different degrees.

In conclusion,

• like terms have to be the same term and same degree.

And that brings us to this topic, to evaluate or simplify the expression with two like terms and one non-like term.

Note that only like terms can evaluate. Let's see some examples:

• 5x+9x would be 14x since they are like terms and thus can be evaluated.
• x+x would be 2x. x is equivalent to 1x so 1x+1x = 2x. They are also like terms as well.

How about a subtraction?

• 9x-2x would be 7x.
• x-x would be 0.
• 10y-7y would be 3y.

But what if it's non-like terms? Simple, we keep it like that!

• 8y+8z would be the same. They are not like terms so they cannot be evaluated.
• 10x-7 would be the same as well. Not like terms.

So to simplify the expression in the question, we evaluate like terms first!

Since 4m and 3m both are like terms. We can do 4m-3m.

$\displaystyle \large{4m + 5 - 3m} \\ \displaystyle \large{4m - 3m + 5}$

Evaluate 4m-3m

$\displaystyle \large{1m + 5}$

We don't usually write 1m so we keep as m instead.

$\displaystyle \large{m + 5}$

Now, can we evaluate m+5? No, because m and 5 are not like terms so we keep like this.

Hence, the answer is m+5