Solve $\dfrac{5 - 2x}{3} \leq \dfrac{x}{6} - 5$.
A$x \geq 8$
B$x \leq 8$
C$x \geq -8$
D$x \leq -8$
Answer & Solution
Correct answer: A. $x \geq 8$
Multiply both sides by 6 (positive — sign preserved):
$2(5 - 2x) \leq x - 30$
$10 - 4x \leq x - 30$
$-5x \leq -40$
Divide by $-5$ (negative — **flip**): $x \geq 8$.
Verify at $x = 8$: LHS $= (5 - 16)/3 = -11/3$. RHS $= 8/6 - 5 = 4/3 - 5 = -11/3$. Equal ✓ (boundary).
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