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3 years ago

How to solve 3x-4(8x-6)=20

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

6 0

3x -4(8x - 6) = 20

3x -32x + 24 = 20

-29x = -4

29x = 4

x = $\frac{29}{4}$ = 7.25

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The correct option is 1.

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Answer: y = (5832/25)*(5/18)^x

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

Explanation:

Any general exponential function is of the form

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Plug in (x,y) = (3,5) and we get

y = a*b^x

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If you plug in (x,y) = (2,18), then we'll get this other equation

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So we have this system of equations

$\begin{cases}5 = ab^3\\18 = ab^2\end{cases}$

From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.

Overall, we end up with b = 5/18

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Use that value of b to find 'a'

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You could use the other equation as well to find 'a'

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Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x

To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.

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