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Which of the following is a solution to $x + x^2 = 1$?
Test each option in $x + x^2 = 1$:
- $x = -1$: $(-1) + (-1)^2 = -1 + 1 = 0 \neq 1$
- $x = 0$: $0 + 0 = 0 \neq 1$
- $x = \dfrac{1}{2}$: $\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} \neq 1$
- $x = 1$: $1 + 1 = 2 \neq 1$
Solving $x^2 + x - 1 = 0$: $x = \dfrac{-1 \pm \sqrt{5}}{2}$, which gives irrational values not among the standard choices. Therefore, none of the listed options is a solution.
Dehydrohalogenation of an alkyl halide is typically carried out with:
Alcoholic KOH (strong base in ethanol) promotes E2 elimination to form alkenes. Aqueous KOH favors substitution; conc. H₂SO₄ can cause elimination but also other reactions; Zn dust is for dehalogenation (vicinal dihalides).
Purchases ledger control account balance: $8,232. Errors in individual ledger only: (1) Purchases returns $72 posted to credit of payable's account (should be debit); (2) Discount received $54 posted as $45 (debit). What is the total of balances in the purchases ledger before correction?
Option D ($8,385) is correct.
Error 1: Returns $72 credited instead of debited → payable's balance overstated by $144 (wrong side = double error).
Error 2: Discount posted as $45 instead of $54 → understated by $9.
Ledger total = $8,232 + $144 + $9 = $8,385
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