This is simply a multi step equation which is very simple to solve; if you know how.
First things first, we are given a variable in this equation and we are asked to solve for this variable. In any given equation, there is one ONE value which will prove the equation to be true. To solve this equation, we need to isolate the variable and then solve.
We have 16x - 5x = 11~~this tells us that "the difference between the product of 16 and some number and the product of 5 and some number is 11"
now to make this equation a little more simple, we are going to COMBINE LIKE TERMS. Combine any like variables together "x's with x's and y's with y's. (if applicable--depending on how many different variables you are working with)
16x - 5x = 11 Combine the x's together--Note that 5x has a minus sign in front of it so we will subtract the 2 variables
11x = 11
Now, we have a number sentence that shows "11 times some number is 11" but I want to know that one number is, not 11 times that number so we will need to get rid of the coefficient. To do this, I usually ask my students what is happening in this equation. This prompts them to analyze the equation and to identify any key indicators as to the operation that is going on in the equation and how to solve it.
Since we are dealing with multiplication, we need to do the opposite; DIVIDE.
We are going to divide both sides by 11 to get the variable "x" by itself as follows
11x = 11
11 11
x = 1
Now, we have a proposed solution to this equation, but lets say we're unsure if we did it correctly. We have the option to "check" our answer by simply plugging the proposed solution back into the original equation to see if we did solve it correctly. If we did do it correctly, we will have a number sentence that is true; both sides will be equal. If both sides do not equal, then we messed up somewhere along the road.
So, lets check ourselves by plugging our proposed solution "1" in for "x"
16x - 5x = 11
16(1) - 5(1) = 11~~Notice how I just changed all of my variables (x) to the proposed solution (1)
16 - 5 = 11~~Evaluate
11 = 11~~Both sides are, in fact, equal. So, x = 1 is the answer to the above equation.
If any of this is still confusing or any questions are still lingering, please feel free to reach out to me, I would love to assist.
Have a Wonderful Day!!
--Michael D.
