5 – 6x = 8x + 17

Answer 1

Hi George!

The goal of this problem is to solve for x. The approach I would take is to move like terms to opposite sides of the equal sign. This means having x-containing terms (6x and 8x) on one side and whole numbers (5 and 12) on the other side of the equal sign.

1) Subtract 5 from both sides and then subtract 8x from both sides.

5 - 6x - 5 = 8x + 17 - 5

-6x = 8x + 12

then

-6x - 8x = 8x + 12 - 8x

-(6x+8x) = 12

-14x = 12

Due to the distributive property, -6x-8x is the same as writing -(6x+8x), so this may help if its easier for you to visualize adding numbers instead of subtracting negative numbers.

2) The last step is to isolate x to get your final answer; to simplify the fraction, divide the numerator and denominator by a common factor, which in this case is two.

-14x/-14 = 12/-14

x = -12/14

x = -(12/2)/(14/2)

x = -6/7 is your final answer!

As a reminder, due to the associative property, -12/14 is equal to 12/-14.

Let me know if you have any questions about the steps I took or the words I used!

Answer 2

5-6x=8x+7

-7 +6

-2 =14x

-1/7 =x

or x=-14.285...............

Answer 3

We want to rearrange this equation so that we solve for x. Our final answer should look something like "x = a number"

Start by adding 6x to both sides to combine the terms including "x":

5 - 6x = 8x + 17

+6x +6x

5 = 14x + 17

Now we want to combine the numbers, also called constants. Subtract 17 from both sides

5 = 14x + 17

-17 -17

-12 = 14x

Divide both sides by 14 to get x by itself

-12/14 = 14x/14

-12/14 = x

Simplify the fraction

-6/7 = x

Final answer:

x = -6/7