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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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Step-by-step explanation:

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3 years ago
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= 8

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Read 2 more answers
Help im trying to get better grades
ioda

Answer:

<u><em> </em></u><u><em>Blank 1:</em></u><u><em> </em></u>\tt{(1\frac{5}{7},-1) }<u><em /></u>

<u><em> Blank 2:</em></u><u><em> </em></u>\tt{(-1\frac{5}{7},1) }

Step-by-step explanation:

<em>To find the reflection over the x-axis and y-axis:</em>

<em>As we know, the image of the point (x,y) under a reflection over the x-axis is (x,−y).</em>

<em>So, we get,</em>

\tt{(-1\frac{5}{7},1) }

So, the answers are,

Blank 1 :&#10;\tt{(1\frac{5}{7},-1) }&#10;&#10;

Blank 2: &#10;\tt{(-1\frac{5}{7},1) }&#10;&#10;

<em>I hope this Helps you!</em>

<em>If you have any questions let me know!</em>

4 0
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