Pregunta
QUESTION 1: Prior knowledge 1.1 Given the following linear inequality: \( -6<2 x-4 \leq 2 \) 1.1.1 Solve the linear inequality.
Ask by Barber Moreno. in South Africa
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The solution to the inequality is \( -1 < x \leq 3 \).
Solución
To solve the linear inequality:
\[
-6 < 2x - 4 \leq 2
\]
**Step 1: Add 4 to all parts of the inequality**
This will help isolate the term with \( x \).
\[
-6 + 4 < 2x - 4 + 4 \leq 2 + 4
\]
\[
-2 < 2x \leq 6
\]
**Step 2: Divide all parts by 2**
This will solve for \( x \).
\[
\frac{-2}{2} < \frac{2x}{2} \leq \frac{6}{2}
\]
\[
-1 < x \leq 3
\]
**Final Solution:**
\[
x \in (-1, \, 3]
\]
This means that \( x \) is greater than **-1** and less than or equal to **3**.
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Simplifique esta solución Mind Expander
To solve the linear inequality \( -6 < 2x - 4 \leq 2 \), we can break it down into two parts. First, we'll solve \( -6 < 2x - 4 \): 1. Add 4 to all sides: \( -2 < 2x \) 2. Divide by 2: \( -1 < x \) or \( x > -1 \). Next, we solve \( 2x - 4 \leq 2 \): 1. Add 4 to both sides: \( 2x \leq 6 \) 2. Divide by 2: \( x \leq 3 \). Finally, combine the results: \( -1 < x \leq 3 \). So the solution in interval notation is \( (-1, 3] \). To sum it all up, the solution to the inequality \( -6<2x-4\leq 2 \) simply tells us that x can take on values greater than -1 but less than or equal to 3. Nice and tidy!
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