Solve the exponential equation $4^{x + 1} = 8^{x - 1}$ for $x$ .

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In algebra, what is the solution set of the linear equation $3 (2 x - 5) + 4 = 5 x - 7$ over real numbers?
In coordinate geometry, what is the distance between the points $A (- 2, 3)$ and $B (4, - 5)$ in the Cartesian plane?
What is the exact value of the logarithmic expression $lo g_{2} (32) - lo g_{3} (81) + ln (e^{4})$ ?
In trigonometry, which value equals $sin (\frac{7 π}{6})$ ?
A geometric sequence has first term $a_{1} = 3$ and common ratio $r = 2$ . What is the sum of its first $6$ terms?
What is the derivative of the polynomial function $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ at $x = 2$ ?