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Fed [463]
3 years ago
9

Anna is given the equation 3 + 2x = 2x + 3 The replacement set is {2, 3, 4, 5} Anna says the solution is {3}, but the teacher ma

rked her problem incorrect. Explain what the answer should be and why. Why do you think this is?
Mathematics
1 answer:
alexira [117]3 years ago
5 0

<u><em>Answer:</em></u>

The given equation has <u>infinite number of solutions</u>. This means that <u>any real number</u> can be considered a solution to the given equation.

Since the given replacement set {2,3,4,5} consists of real numbers, therefore, the whole set is considered as a solution to the given equation.

This is because, when solving the given equation for x, we will end up with 0 = 0, this means that whatever the value of x is, both sides of the equation will always be equal.

<u><em>Explanation:</em></u>

To solve for x, we need to isolate the x on one side of the equation.

<u>This can be done as follows:</u>

3 + 2x = 2x + 3 (subtract 3 from both sides)

2x = 2x (subtract 2x from both sides)

0 = 0

This means that whatever, the value of x is, both sides of the equation will be equal. This means that all real numbers are considered a solution for this equation.

<u>Let's verify this using the given replacement set {2,3,4,5}:</u>

<u>For x = 2: </u>

Left hand side: 3 + 2(2) = 3 + 4 = 7

Right hand side: 2(2) + 3 = 4 + 3 = 7

Both sides are equal.

<u>For x = 3:</u>

Left hand side: 3 + 2(3) = 3 + 6 = 9

Right hand side: 2(3) + 3 = 6 + 3 = 9

Both sides are equal.

<u>For x = 4:</u>

Left hand side: 3 + 2(4) = 3 + 8 = 11

Right hand side: 2(4) + 3 = 8 + 3 = 11

Both sides are equal.

<u>For x = 5:</u>

Left hand side: 3 + 2(5) = 3 + 10 = 13

Right hand side: 2(5) + 3 = 10 + 3 = 13

Both sides are equal.

Hope this helps :)


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Using a linear function, it is found that the algebraic expression that shows the amount Ms. Jackson will pay for the small truck for the week is:

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<h3>What is a linear function?</h3>
  • A linear function is modeled by:

y = ax + b

In which:

  • a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
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In this problem:

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Then, the expression is:

y(m) = 0.6m + 340

To learn more about linear function, you can take a look at brainly.com/question/25823744

8 0
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50 points ! marking brainly to whoever gets all 5 correct !
Svetradugi [14.3K]

1. 5

2. 7-3 root 3

3. 6

4. 4.24

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