Answer:
See below.
Step-by-step explanation:
So, we know that Noah's purchase can be modeled by the equation:
![x-0.1x+2.70=56.70](https://tex.z-dn.net/?f=x-0.1x%2B2.70%3D56.70)
Part 1)
The solution to the equation will be the value of x.
In this case, x will represent the original price of the jeans.
We know that Noah has a coupon for 10% off the <em>original price of the jeans</em>.
So, 0.1x will represent how much of the original price Noah gets a a discount on.
Therefore, (x - 0.1x) represents the total cost of the jeans <em>after</em> the coupon.
So, x is our original price of the jeans.
Part 2)
To verify that 70 is <em>not</em> a solution, we can simply substitute 70 for x and check whether or not the equation is true. So:
![(70)-0.1(70)+2.7\stackrel{?}{=}56.70](https://tex.z-dn.net/?f=%2870%29-0.1%2870%29%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D56.70)
Multiply:
![70-7+2.7\stackrel{?}{=}56.7](https://tex.z-dn.net/?f=70-7%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D56.7)
Subtract:
![63+2.7\stackrel{?}{=}56.7](https://tex.z-dn.net/?f=63%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D56.7)
Add:
![65.7\neq56.7](https://tex.z-dn.net/?f=65.7%5Cneq56.7)
However, we <em>can</em> verify that 60 <em>is</em> the solution by substituting. So, substitute 60 for every x:
![(60)-0.1(60)+2.7\stackrel{?}{=}5.7](https://tex.z-dn.net/?f=%2860%29-0.1%2860%29%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D5.7)
Multiply:
![60-6+2.7\stackrel{?}{=}56.7](https://tex.z-dn.net/?f=60-6%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D56.7)
Subtract:
![54+2.7\stackrel{?}{=}56.7](https://tex.z-dn.net/?f=54%2B2.7%5Cstackrel%7B%3F%7D%7B%3D%7D56.7)
Add:
![56.7\stackrel{\checkmark}{=}56.7](https://tex.z-dn.net/?f=56.7%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D56.7)
So, 60 is indeed the solution and is the value of x.
So, this means that $60 was the original price of the jeans.