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faltersainse [42]
3 years ago
14

How many solutions are there to the equation below? 8x + 47 = 8(x + 5)

Mathematics
1 answer:
qaws [65]3 years ago
4 0

Answer:

there are 0 solutions to the equation

Step-by-step explanation:

To know how many solutions are in the problem, we have to solve for x and see what result we have left. According to the result, we will know how many solutions there are

8x + 47 = 8(x + 5)

8x + 47 = 8*x + 8*5

8x + 47 = 8x + 40

8x - 8x = 40 - 47

0 = -7

As we can see we are left with an equality that is not fulfilled, this means that there is no solution to the problem, at least in the field of real numbers

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Answer:

The exact answer in terms of radicals is x = 5*\sqrt[3]{25}

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===============================================

Work Shown:

Let y = \sqrt[5]{x^3}

So the equation reduces to  -7  = 8-3y

Let's solve for y

-7 = 8-3y

8-3y = -7

-3y = -7-8 ... subtract 8 from both sides

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y = 5

-----------

Since y = \sqrt[5]{x^3} and y = 5, this means we can equate the two expressions and solve for x

y = 5

\sqrt[5]{x^3} = 5

x^3 = 5^5 Raise both sides to the 5th power

x^3 = 3125

x = \sqrt[3]{3125} Apply cube root to both sides

x = \sqrt[3]{125*25}

x = \sqrt[3]{125}*\sqrt[3]{25}

x = \sqrt[3]{5^3}*\sqrt[3]{25}

x = 5*\sqrt[3]{25}

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