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sashaice [31]
3 years ago
15

Which number line represents the solution of 4 - 3x > 13?

Mathematics
1 answer:
Oksanka [162]3 years ago
5 0

Answer:

x

Step-by-step explanation:

Given inequality:

4-3x>13

In order to represent the solution on the number line, we will first solve the given inequality.

We have

4-3x>13

Subtracting both sides by 4.

4-3x-4>13-4

-3x>9

Dividing both sides by -3.

\frac{-3x}{-3} [On dividing both sides by a negative number the sign of the inequality reverses.]

x

So, solution of this inequality will range from -3 to -∞

The number line is represented below.

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"Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an acute triangle.
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1^o\\5\leq10\leq x\\\\\left\{\begin{array}{ccc}5+10 \ \textgreater \  x\\5^2+10^2 \ \textgreater \  x^2\end{array}\right\to\left\{\begin{array}{ccc}x \ \textless \  15\\ x^2 \ \textless \  125\end{array}\right\to\left\{\begin{array}{ccc}x \ \textless \  15\\ x \ \textless \  \sqrt{125}\approx11.1\end{array}\right\\\\\boxed{x=11}\\\\2^o\\5\leq x\leq10\\\\\left\{\begin{array}{ccc}5+x \ \textgreater \  10\\ 5^2+x^2 \ \textgreater \  10^2\end{array}\right\to\left\{\begin{array}{ccc}x \ \textgreater \  5\\ x^2 \ \textgreater \  75\end{array}\right\to\left\{\begin{array}{ccc}x \ \textgreater \  5\\ x \ \textgreater \  \sqrt{75}\approx8.7\end{array}\right\\\boxed{x=9}

3^o\\x\leq5\leq10\\\\\left\{\begin{array}{ccc}x +5 \ \textgreater \  10\\ x^2+5^2 \ \textgreater \  10^2\end{array}\right\to\left\{\begin{array}{ccc}x \ \textgreater \ 5\\ x^2 \ \textgreater \ 75\end{array}\right\to\left\{\begin{array}{ccc}x \ \textgreater \ 5\\ x \ \textgreater \ \sqrt{75}\approx8.7\end{array}\right\\\boxed{x\in\O}\\\\Answer:\boxed{x=9\ or\ x=11}\to your\ answer:\boxed{\boxed{x=11}}
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Question 5
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