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When the equation a – bx = cx + d is solved for x, the result is x = .


Use the general solution to solve 5 – 6x = 8x + 17.

Verified Answer :

The correct answer is:

x=6/7.

Explanation:

First we find the general form by solving for x:

a-bx = cx+d

Subtract a from each side:

a-bx-a = cx+d-a

-bx = cx+d-a

Subtract cx from each side:

-bx-cx = cx+d-a

-bx-cx = d-a

We can divide both sides by -1:

(-bx-cx)/-1 = (d-a)/-1

bx+cx = -d+a

bx+cx = a-d

Factor out an x on the left:

x(b+c) = a-d

Divide both sides by (b+c):

(x(b+c))/(b+c) = (a-d)/(b+c)

x = (a-d)/(b+c)

In this equation, a = 5, b = 6, c = 8 and d = 17:

x = (5-17)/(6+8) = -12/14

This simplifies to -6/7.

The value of x in the equation a – bx = cx + d is = a - d / c + b

The value of x in the equation  5 – 6x = 8x + 17 is - 6 / 7

a - bx = cx + d

add bx to both sides of the equation

a - bx + bx = cx + bx + d

a = cx + bx + d

subtract d form both sides of the equation

a - d = cx + bx + d - d

a - d = cx + bx

Distributive law:

using distributive law on the right side of the equation

a - d = x (c + b)

divide both sides by (c + b)

Therefore,

x = a - d / c + b

Let's use the same method to solve 5 – 6x = 8x + 17

5 – 6x = 8x + 17

add 6x to both sides

5 – 6x  + 6x= 8x + 6x + 17

5 = 14x + 17

subtract 17 from both sides

5 - 17 = 14x + 17 - 17

-12 = 14x

divide both sides by 14

x = -12 / 14

x = - 6 / 7

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