Solve for x 6^5x-4=6^4x

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

5 0

Answer:

x = 4

Step-by-step explanation:

6^5x-4=6^4x

6^ (5x-4) = 6^ (4x)

Dividing through by 6

5x - 4 = 4x

Collecting Like Terms

5x - 4x = 4

x = 4

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two years ago a man was six times as old as his daughter. In 18 years he will be twice as old as her, determine their present ag

BabaBlast [244]

Step-by-step explanation:

Let m = man's age right now

d = daughter's age right now

m-2 = 6(d-2) => m = 6d -12 +2 = 6d-10

m+18 = 2(d+18) => m = 2d+36-18 = 2d+18

6d-10 = 2d+18

4d = 28

d = 7

m = 32

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3 years ago

8/x-5 - 9/x-4 = 5/x^2-9x+20

adelina 88 [10]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2752942

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Solve the equation:

$\mathsf{\dfrac{8}{x-5}-\dfrac{9}{x-4}=\dfrac{5}{x^2-9x+20}\qquad\qquad(x\ne 5~and~x\ne 4)}$

Reduce the fractions at the left side so that they have the same denominator:

$\mathsf{\dfrac{8(x-4)}{(x-5)(x-4)}-\dfrac{9(x-5)}{(x-4)(x-5)}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-4x-5x+20}-\dfrac{9x-45}{x^2-4x-5x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32}{x^2-9x+20}-\dfrac{9x-45}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}\\\\\\
\mathsf{\dfrac{8x-32-(9x-45)}{x^2-9x+20}=\dfrac{5}{x^2-9x+20}}$

Numerators must be equal:

$\mathsf{8x-32-(9x-45)=5}\\\\
\mathsf{8x-32-9x+45=5}\\\\
\mathsf{8x-9x=5+32-45}\\\\
\mathsf{-x=-8}\\\\
\mathsf{x=8}\quad\longleftarrow\quad\textsf{this is the solution.}$

I hope this helps. =)

Tags: <em>rational equation fraction solution algebra</em>

7 0

3 years ago

18 less than 3 times d is -27

Reil [10]

3d-18=-27
3d=-27+18
3d= -9
D= -9/3
D=-3

D equals -3. Hope this helps!

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4 years ago

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