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scoray [572]
3 years ago
13

Solve for x: 1/2x + 1/3x - 4 = 5/6(x + 6)

Mathematics
1 answer:
kobusy [5.1K]3 years ago
7 0

Answer:

No solution

Step-by-step explanation:

Lets start by simplifying everything out, and then try to get all of the x's on one side of the equation.

1/2x + 1/3x - 4 = 5/6(x+6)

Simplify and distributive property

5/6x - 4 = 5/6x + 5

Lets subtract 5/6x from both sides to try and get rid of the x from the right side of the equation. (Now, as you may already see, is we try to get all of the x's on one side of the equation, the x's will cancel out, and we will be left with no solution.)

5/6x - 4 - 5/6x = 5/6x + 5 - 5/6x

Simplify

-4 = 5

Because we ended up with something in the form a = b and a ≠ b, there is no solution. (If a = b, then there would be an infinite number of solutions.)

I hope you find this helpful. Let me know if anything in my answer confuses you. Happy studying.

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A savings account is started with an initial deposit of $700. The account earns 1.5% interest compounded
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Answer:

  (a)  A = 700×1.015^t

  (b)  36.2 years

Step-by-step explanation:

(a) Each year, the account value is multiplied by (1 + 1.5%) = 1.015. Repeated multiplication is signified using an exponent. In t years, when the account has been multiplied by 1.015 t times, the account value will be ...

  A = $700×1.015^t

__

(b) You want to find t when A=$1200. Logarithms are involved.

  1200 = 700×1.015^t . . . . use 1200 for A

  1200/700 = 1.015^t . . . . . divide by 700

  log(12/7) = t×log(1.015) . . . . . take logarithms

  log(12/7)/log(1.015) = t ≈ 36.2 . . . . divide by the coefficient of t

It will take about 36.2 years for the account balance to reach $1200.

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