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romanna [79]
2 years ago
13

Indicate whether each of the following equations is sure to have a solution set of all real numbers. Explain your

Mathematics
1 answer:
zlopas [31]2 years ago
4 0

Answer:

a) 0 = -2 is not a valid equality. So a) will not have a solution set of all real numbers.

b) 0 = 0 is a valid equality for all real numbers. So b) will have a solution set of all real numbers.

c) 0 = 0 is a valid equality for all real numbers. So c) will have a solution set of all real numbers.

d) 24x^{3} = 72x^{3} is only valid for x = 0. So d) will not have a solution set of all real numbers.

Step-by-step explanation:

a)

3(x+1) = 3x + 1

3x + 3 = 3x + 1

3x - 3x = 1 - 3

0 = -2

0 = -2 is not a valid equality. So a) will not have a solution set of all real numbers.

b)

x + 2 = 2 + x

x - x = 2 - 2

0 = 0

0 = 0 is a valid equality for all real numbers. So b) will have a solution set of all real numbers.

c)

4x(x+1) = 4x + 4x^{2}

4x^{2} + 4x = 4x + 4x^{2}

4x^{2} - 4x^{2} = 4x - 4x

0 = 0

0 = 0 is a valid equality for all real numbers. So c) will have a solution set of all real numbers.

d)

3x(4x)(2x) = 72x^{3}

24x^{3} = 72x^{3}

This is only valid for x = 0. So d) will not have a solution set of all real numbers.

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