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Elden [556K]
3 years ago
5

Nigel makes the claim that x=6 is the solution to the equation 4(5x−12)−7x=5x. His work to support his claim follows. Given: 4(5

x−12)−7x=5x Step 1: 20x−48−7x=5x Step 2: 20x−7x−48=5x Step 3: 13x−48=5x Step 4: 13x−13x−48=5x−13x Step 5: 0−48=−8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.
Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,

Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,

Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,

Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,

Step 6 is justified by the Associative Property.
Mathematics
1 answer:
RSB [31]3 years ago
5 0

Answer:

Step 1 is justified by the Distributive Property.

Step 4 is justified by the Symmetric Property

Step-by-step explanation:

Given the equation solved by Nigel expressed as

4(5x−12)−7x=5x.

First, we need to expand the bracket using the distributive property

4(5x−12)−7x=5x.

4(5x)-4(12) -7x = 5x

20x - 48 - 7x = 5x

Hence Step 1 is justified by the Distributive Property.

Next is to collect the like terms;

20x - 7x - 48 = 5x

Take the difference

13x - 48 = 5x

Next is to subtract 13x from both sides according to the symmetric property

13x - 48 - 13x = 5x - 13x

Hence Step 4 is justified by the Symmetric Property

The resulting equation will be

0-48 = -8x

Divide both sides by -8

-48/-8 = -8x/-8

6 = x

Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property

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Step-by-step explanation:

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\bar X_1 represent the sample for the sample 1

\bar X_2 represent the sample for the sample 2

s_1 represent the deviation for the sample 1

s_2 represent the deviation for the sample 2  

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n_2 = 81 represent the sample size for the group 2

And on this case if we create the system of hypothesis we have this:

Null hypothesis :\mu_1 -\mu_2 \leq 0

Alternative hypothesis: \mu_1 -\mu_2 >0

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

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Solution to the problem

We assume that we have the following statistics:

\bar X_1 represent the sample for the sample 1

\bar X_2 represent the sample for the sample 2

s_1 represent the deviation for the sample 1

s_2 represent the deviation for the sample 2  

n_1 = 81 represent the sample size for the group 1

n_2 = 81 represent the sample size for the group 2

And on this case if we create the system of hypothesis we have this:

Null hypothesis :\mu_1 -\mu_2 \leq 0

Alternative hypothesis: \mu_1 -\mu_2 >0

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Answer:

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