High School

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Part 1:
A cardboard box, which weighs 0.6 pounds when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation [tex]0.6 + 15b + 4 = 25.6[/tex].

Select all equations that are also equivalent to [tex]0.6 + 15b + 4 = 25.6[/tex].

Responses:

Equation A: [tex]15b + 4 = 25.6[/tex]

Equation B: [tex]15b + 4 = 25[/tex]

Equation C: [tex]3(0.6 + 15b + 4) = 76.8[/tex]

Equation D: [tex]15b = 25.6[/tex]

Equation E: [tex]15b = 21[/tex]

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Part 2:
To solve the equation [tex]7.5d = 2.5d[/tex], Lin divides each side by [tex]2.5d[/tex], and Elena subtracts [tex]2.5d[/tex] from each side.

a. Will both moves lead to the solution? Explain your reasoning.

b. What is the solution?

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Part 3:
The equation [tex]4(x - 2) = 100[/tex] is a true equation for a particular value of [tex]x[/tex]. Explain why [tex]2(x - 2) = 50[/tex] is also true for the same value of [tex]x[/tex].

Answer :

2(x -2) = 50 is also true for the same value of x.

Given,

Part 1:

When a cardboard box is empty, its weight is 0.6 pounds.

It is filled with 15 bags of beans and a 4-pound bag of rice.

The total weight of the box and the contents inside it is 25.6 pounds.

Let the weight of 15 bean bags is 15b. The given scenario can be represented by the equation as follows :

0.6+15b+4=25.6 ....(A)

Taking like terms together,

15b=25.6-0.6-4 ...(1)

15b = 21 ....(2)

Equation (1) or (2) can be the equivalent equation for the equation (A).

Part 2:

Solve the equation:

7.5d = 2.5d, Lin divides each side by 2.5d,

and Elena subtracts 2.5d from each side.

Now, 7.5d/2.5d = 2.5d/2.5d

3 = 1

It is not equal, There is no solution.

a. 7.5d - 2.5d = 2.5d - 2.5d

5d/5 = 0/5

b. What is the solution ?

Solution is d = 0

Part 3:

Given,
The equation 4(x - 2) = 100 is a true equation for a particular value of x.

Explanation: The basic property of the equation is that if you multiply or divide both sides of the equation by the non-zero whole , the equation still holds.

In the Equation : 4 (x - 2) =100 divide by 2 on both sides because 2 is common factor of (4,10)

So, 4(x - 2) =100

1/2 x 4(x-2) = 1/2 x 100

= 2(x-2) = 50

Above all, 2(x -2) = 50 is also true for the same value of x.

Hence, 2(x -2) = 50 is also true for the same value of x.

Learn more about Equations at:

https://brainly.com/question/10413253

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