Question

1. kran says that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. write a convincing explanation as to why this is true.
2. the entrepreneurship club is ordering potted plants for all 36 of its sponsors. one store charges $8.50 for each plant plus a delivery fee of $20. the equation 320 = x + 7.50(36) represents the cost of ordering potted plants at a second store. what does the x represent in this situation? a. the cost for each potted plant at the second store b. the delivery fee at the second store c. the total cost of ordering potted plants at the second store d. the number of sponsors of the entrepreneurship club (from unit 2, lesson 4.)
3. which equation is equivalent to the equation 5x + 30 = 45? a. 35x = 45 b. 5x = 75 c. 5(x + 30) = 45 d. 5(x + 6) = 45 (from unit 2, lesson 6.)

Explanation:

4.

Step1: Analyze the first - equation

The equation $x + 4=20$.

Step2: Analyze the second - equation

The equation $5(x + 4)=100$. Divide both sides of $5(x + 4)=100$ by 5, we get $\frac{5(x + 4)}{5}=\frac{100}{5}$, which simplifies to $x + 4 = 20$. So, any solution of $x+4 = 20$ is also a solution of $5(x + 4)=100$ because the second equation is just a multiple of the first equation.

5.

The total cost of ordering plants at the second store is composed of the cost of the plants and the delivery fee. The cost of 36 plants at $7.50$ each is $7.50\times36$. The total cost is 320. So, $x$ represents the delivery fee.

Step1: Factor the left - hand side of the original equation

Given $5x+30 = 45$. Factor out 5 from the left - hand side. Since $5x+30=5\times x+5\times6$, by the distributive property $a\times(b + c)=a\times b+a\times c$, we can rewrite $5x + 30$ as $5(x + 6)$. So the equivalent equation is $5(x + 6)=45$.

Answer:

B. The delivery fee at the second store

6.