Question

What is the solution to this question?

Answer 1

Explanation:

To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:

(-1)(x+4) = 2(x-5)

Expanding both sides and simplifying, we get:

-x - 4 = 2x - 10

Bringing all the x terms to one side and all the constant terms to the other, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:

(-1)/(2-5) = 2/(2+4)

Simplifying, we get:

1/3 = 1/3

Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.

Answer 2

Answer: x = 2

Explanation:

`\boldsymbol{\sf{The\:exercise\:is \longmapsto \ (-1)/(x-5)=(2)/(x+4) }}`

We cross multiply.

-(x + 4) = 2(x - 5)

We apply the multiplicative law of distribution.

-x -4 = 2(x - 5)

-x - 4 = 2x - 10

We rearrange the unknown terms to the left side of the equation.

-x - 2x = -10 + 4 <===Combine as terms===> -3x = -10 + 4

We calculate -10 + 4 = -6.

-3x = -6

We divide both sides of the equation by the coefficient of the variable.

`\boldsymbol{\sf{x=(-6)/(-3) \iff \ x=(6)/(3) }}`

x = 2