Question

I need help please !!

Answer 1

`\large{\bf Step-by-step~explanation:}`

Since we are solving for x, our goal is to isolate the variable.

`\bf Step~1:`

To solve, we have to cross multiply these fractions. We do this by multiplying 2 by (x - 4), and 3 by (3x + 9).

`\bf 2*x-4=2x-8\\3*3x+9= 9x+27`

`\bf Step~2:`

After that, we replace the fractions with the expressions.

`\bf 2x-8=9x+27`

`\bf Step~3:`

Since our goal is to isolate the variable x, we cannot have two variables, one on each side. To end up with only one, we either subtract 9x from both sides or 2x from both sides, to cancel one of the values out. I am going to choose 2x because when you subtract 2x from 9x, you will not end up with a negative number.

`\bf 2x(-2x)-8=9x(-2x)+27\\-8=7x+27`

`\bf Step~4:`

Now, we have to subtract 27 from both sides to get the term with the variable by itself.

`\bf-8(-27)=7x+27(-27)\\-35=7x`

*on these demonstrations, the numbers in parenthesis means to add/subtract, not multiply.

`\bf Step~5 ~(Final~step!):`

Finally, we divide both sides by 7 to get x's value.

`\bf (-35)/(7) =(7x)/(7)`

`\bf -5=x`

`\large\boxed{\bf Our~final~answer:~x=-5; ~B}`

Answer 2

B

Explanation:

So we have the equation:

`(3x+9)/(2)=(x-4)/(3)`

First, let's get rid of the fractions. We can multiply by the LCM of 2 and 3 which is 6. So, multiply both sides by 6:

`6((3x+9)/(2))=6((x-4)/(3))`

On the left, the 6 and 2 cancel, leaving a 3.

On the right, the 6 and 3 cancel, leaving a 2.

So:

`3(3x+9)=2(x-4)`

Distribute:

`9x+27=2x-8`

Subtract 2x from both sides:

`7x+27=-8`

Subtract 27 from both sides:

`7x=-35`

Divide both sides by 7:

`x=-5`

And we're done!

The value of x is -5.

Our answer is B.