(25, C2) Tentukan himpunan penyelesaian dari pertaksanaan berikut dan tuliskan
solusinya dalam notasi selang:

Ask by Brooks Santiago. in Indonesia

Dec 07,2024

Question

(25, C2) Tentukan himpunan penyelesaian dari pertaksanaan berikut dan tuliskan solusinya dalam notasi selang: $$ \begin{array}{ll}	ext { a. }-7<3 x-\frac{1}{2} \leq 10 ; & 	ext { b. }\left|\frac{2 x-3}{5}-\frac{x}{3}ight|>1 \ 	ext { c. } \frac{2 x-5}{x-4} \leq 1\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ -7<3x-\frac{1}{2} \leq 10 $$. Solve the system of inequalities by following steps: - step0: Solve for $$x$$: $$\left\{ \begin{array}{l}-7<3x-\frac{1}{2}\3x-\frac{1}{2}\leq 10\end{array} ight.$$ - step1: Solve the inequality: $$\left\{ \begin{array}{l}x>-\frac{13}{6}\x\leq \frac{7}{2}\end{array} ight.$$ - step2: Find the intersection: $$-\frac{13}{6}1 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$\left|\frac{2x-3}{5}-\frac{x}{3} ight|>1$$ - step1: Calculate the absolute value: $$\frac{1}{15}\left|x-9 ight|>1$$ - step2: Rewrite the expression: $$\frac{\left|x-9 ight|}{15}>1$$ - step3: Multiply both sides: $$\left|x-9 ight|>15$$ - step4: Separate into possible cases: $$\begin{align}&x-9>15\&x-9<-15\end{align}$$ - step5: Solve the inequality: $$\begin{align}&x>24\&x<-6\end{align}$$ - step6: Find the union: $$x \in \left(-\infty,-6 ight)\cup \left(24,+\infty ight)$$ Solve the equation $$ \frac{2x-5}{x-4} \leq 1 $$. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$\frac{2x-5}{x-4}\leq 1$$ - step1: Find the domain: $$\frac{2x-5}{x-4}\leq 1,x eq 4$$ - step2: Move the expression to the left side: $$\frac{2x-5}{x-4}-1\leq 0$$ - step3: Subtract the terms: $$\frac{x-1}{x-4}\leq 0$$ - step4: Set the numerator and denominator of $$\frac{x-1}{x-4}$$ equal to 0$$:$$ $$\begin{align}&x-1=0\&x-4=0\end{align}$$ - step5: Calculate: $$\begin{align}&x=1\&x=4\end{align}$$ - step6: Determine the test intervals: $$\begin{align}&x<1\&14\end{align}$$ - step7: Choose a value: $$\begin{align}&x_{1}=0\&x_{2}=3\&x_{3}=5\end{align}$$ - step8: Test the chosen value: $$\begin{align}&x<1 extrm{ } extrm{is not a solution}\&14 extrm{ } extrm{is not a solution}\end{align}$$ - step9: Include the critical value: $$\begin{align}&1\leq x<4 extrm{ } extrm{is the solution}\end{align}$$ - step10: The final solution is $$1\leq x<4:$$ $$1\leq x<4$$ - step11: Check if the solution is in the defined range: $$1\leq x<4,x eq 4$$ - step12: Find the intersection: $$1\leq x<4$$ a. Solusi dari pertaksanaan $$ -7<3x-\frac{1}{2} \leq 10 $$ adalah $$ -\frac{13}{6} < x \leq \frac{7}{2} $$. b. Solusi dari pertaksanaan $$ \left|\frac{2x-3}{5}-\frac{x}{3} ight|>1 $$ adalah $$ x \in (-\infty,-6) \cup (24,+\infty) $$. c. Solusi dari pertaksanaan $$ \frac{2x-5}{x-4} \leq 1 $$ adalah $$ 1 \leq x < 4 $$. a. $$ -\frac{13}{6} < x \leq \frac{7}{2} $$ b. $$ x \in (-\infty,-6) \cup (24,+\infty) $$ c. $$ 1 \leq x < 4 $$

(25, C2) Tentukan himpunan penyelesaian dari pertaksanaan berikut dan tuliskan
solusinya dalam notasi selang:

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