1. ## writing inequalities

Write an inequality to describe the possible values of x.

2. Easy, just use the Pythagorean theorem. It states that for a right triangle, two legs both squared and summed equals the hypotenuse squared. A wider angle makes way to a longer hypotenuse, so our theorem is adjusted:

$\displaystyle a^2+b^2 \le c^2$

We then have...

$\displaystyle (5x+3)^2 + 25x^2 \le c^2$

and...

$\displaystyle (3x+17)^2 + 25x^2 \le c^2$

BTW, I don't understand from the drawing how two sides are equal (5x)? Nevertheless, I will continue with the algebra.

$\displaystyle (5x+3)^2 + 25x^2 = (3x+17)^2 + 25x^2$
$\displaystyle 5x+3=3x+17$
$\displaystyle 2x=14$
$\displaystyle x=14$

3. Thank you, and the drawing is not drawn to scale, not even the one given to me originally was drawn to scale...

I think it is supposed to be one of the "0 < x < 4" thingies though...

4. Originally Posted by Melancholy
Write an inequality to describe the possible values of x.

note, that there was a $\displaystyle 90^o$ and was divided into $\displaystyle 60^o$ and $\displaystyle 30^o$.. so, 30 + 95 = 125 subtracted from 180 gives 55.. thus, $\displaystyle 3x + 17 > 5x$, which implies $\displaystyle 2x < 17$ or $\displaystyle x < 8.5$
for the lower bound, we have x cannot be non-positive, otherwise, we would have a negative o zero length given by 5x.. thus, we can assume that $\displaystyle 0 < x < 8.5$