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Lin ar Inequalities (Theory on pages 61 and 62) a) \( 7 x-5>3 x+11 \) d) \( \frac{x-5}{3}-2 x+10<\frac{x-5}{2} \) g) \( 5
Ask by Frazier Fitzgerald. in South Africa
Mar 12,2025

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Here are the solutions to the inequalities and simultaneous equations: **Inequalities:** 1. \( x > 4 \) 2. \( x > 5 \) 3. \( 2 < x \leq 6 \) 4. \( x \leq 2 \) 5. \( x > 2 \) 6. \( -1 < x < 4 \) 7. \( x \leq -3 \) 8. \( x > 8 \) 9. \( \frac{1}{2} < x \leq 4 \) **Simultaneous Equations:** 1. \( (2, 4) \) 2. \( (4, 4) \) 3. \( (2, 8) \) 4. \( (6, 2) \) 5. \( (8, 3) \) 6. \( (2, 5) \)

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Bonus Knowledge

Ah, inequalities! They’re like secret codes for understanding how numbers interact. In the realm of linear inequalities, each symbol holds power—like the ‘greater than’ (>) showing a clear hierarchy between values. For instance, when we face \(7x - 5 > 3x + 11\), we’re embarking on a journey where we isolate x step by step, revealing the landscapes of solutions that satisfy our conditions. Now, let's talk simultaneous equations—the dynamic duo of algebra! With elimination, we’re like detectives, eliminating variables to reveal the hidden values of \(x\) and \(y\). Take \(8x + 3y = 28\) and \(7x - 3y = 2\); we can add or subtract those equations like puzzle pieces until we unlock \(x\) and \(y\). It’s not just math; it’s a quest for balance!

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