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yuradex [85]
3 years ago
12

Solve. −4/3x+1/6<7/9

Mathematics
2 answers:
boyakko [2]3 years ago
6 0
 <span>x > -11/24 is the answer

</span>
Korvikt [17]3 years ago
4 0
Let's solve your inequality step-by-step.<span><span><span><span><span>−4</span>3</span>x</span>+<span>16</span></span><<span>7<span>9

</span></span></span>Step 1: Subtract 1/6 from both sides.<span><span><span><span><span><span>−4</span>3</span>x</span>+<span>16</span></span>−<span>16</span></span><<span><span>79</span>−<span>16</span></span></span><span><span><span><span>−4</span>3</span>x</span><<span><span>1118
</span>
</span></span>Step 2: Multiply both sides by 3/(-4).<span><span><span>(<span>3<span>−4</span></span>)</span>*<span>(<span><span><span>−4</span>3</span>x</span>)</span></span><<span><span>(<span>3<span>−4</span></span>)</span>*<span>(<span>1118</span>)</span></span></span><span>x><span><span>−11</span><span>24

</span></span></span>Answer:<span>x><span><span><span>−11</span>24</span>
</span></span>
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Between 1000 and 5000 snowboards will make the function AP(x) >0.

Step-by-step explanation:

Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.

In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.

P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:

r_1,r_2 = \frac{-6 ^+_- \sqrt{6^2-4*(-1)*(-5)} }{2*(-1)} = \frac{-6^+_-\sqrt{16}}{-2} = \{1, 5\}

Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:

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3 years ago
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