Question

Which of the following is the solution to 11/(x+2) = 4/(x-1)?

a. 7/19


b. -7/19


c. -19/7


d. 19/7

Answer 1

The solution to the equation 11/(x+2) = 4/(x-1) is x = 19/7.

Step-by-step explanation:

To find the solution to the equation 11/(x+2) = 4/(x-1), we can start by cross-multiplying the equation. This gives us 11(x-1) = 4(x+2).

Simplifying this equation, we get 11x - 11 = 4x + 8. Combining like terms, we have 11x - 4x = 8 + 11. This simplifies to 7x = 19.

Finally, dividing both sides by 7, we find that x = 19/7. So, the solution to the equation is d. 19/7.

The equation given is 11/(x+2) = 4/(x-1). To solve for x, we need to find a common denominator and solve the resulting equation. So, we cross-multiply to get 11(x - 1) = 4(x + 2). Simplifying, we get 11x - 11 = 4x + 8. Then we subtract 4x from both sides to isolate the x terms on one side, obtaining 7x - 11 = 8. Adding 11 to both sides yields 7x = 19. Finally, dividing both sides by 7 gives us x = 19/7. So the correct answer is d. 19/7.

Answer 2

`Solution, (11)/(\left(x+2\right))=(4)/(\left(x-1\right))\quad :\quad x=(19)/(7)\quad \left(\mathrm{Decimal:\quad }x=2.71429\dots \right)`

`Steps:`

`(11)/(\left(x+2\right))=(4)/(\left(x-1\right))`

`\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}(a)/(b)=(c)/(d)\mathrm{\:then\:}a\cdot \:d=b\cdot \:c, 11\left(x-1\right)=\left(x+2\right)\cdot \:4`

`\mathrm{Expand\:}11\left(x-1\right):\quad 11x-11, \mathrm{Expand\:}\left(x+2\right)\cdot \:4:\quad 4x+8, 11x-11=4x+8`

`\mathrm{Add\:}11\mathrm{\:to\:both\:sides}, 11x-11+11=4x+8+11`

`\mathrm{Simplify}, 11x=4x+19`

`\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}, 11x-4x=4x+19-4x`

`Simplify, 7x=19`

`\mathrm{Divide\:both\:sides\:by\:}7, (7x)/(7)=(19)/(7)`

`\mathrm{Simplify}, x=(19)/(7)`

`\mathrm{The\:Correct\:Answer\:is\:D.\:x=(19)/(7)}`

`\mathrm{Hope\:This\:Helps!!!}`

`\mathrm{-Austint1414}`