Solve the proportion x over x plus 1 equals 4 over x plus 4. What is the value(s) of x?

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Answer 1 · 2017-08-08T20:58:27

See a solution process below:

We can write this proportion as:

$x/(x + 1) = 4/(x + 4)$

Next, we can do cross product or cross multiply the equation:

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$x(x + 4) = 4(x + 1)$

$x^2 + 4x = 4x + 4$

We can now put this in standard form:

$x^2 + 4x - color(red)(4x) - color(blue)(4) = 4x - color(red)(4x) + 4 - color(blue)(4)$

$x^2 + 0 - color(blue)(4) = 0 + 0$

$x^2 - color(blue)(4) = 0$

Then, the left side of the equation is a difference of squares so we can factor it as:

$(x + 2)(x - 2) = 0$

Now, to find the values of $x$ we solve each term on the left side for $0$ :

Solution 1

$x + 2 = 0$

$x + 2 - color(red)(2) = 0 - color(red)(2)$

$x + 0 = -2$

$x = -2$

Solution 2

$x - 2 = 0$

$x - 2 + color(red)(2) = 0 + color(red)(2)$

$x - 0 = 2$

$x = 2$

The Solutions Are: $x = -2$ and $x = 2$