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2 years ago

Solve the inequality 17u≥−8, and write the solution in interval notation.

Mathematics

1 answer:

xxTIMURxx [149]2 years ago

8 0

Answer:

u= -8/17 [-8, ∞)

Step-by-step explanation:

solve it like regular equation

17u≥-8

divide 17 on both side

then you get u≥-8/17

so, (u) is any value greater than or equal to -8/17

less than equal means solid dot on number line i think its called also mean ([) meaning it includes this value too. It is a multiplication so it can be any number above -8 or -8 itself. Thus, the interval notation will be [-8, ∞). Infinite is not a fix number so we use this (). hope this helps good luck

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2 years ago

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You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

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2 years ago