Discussion

The value of x which satisfies the equation

10(x + 6) + 8(x - 3) = 5(5x - 4)

also satisfies the equation

Answer: D

The solution, x = 8, also satisfies 5(x - 5) = 2(x - 3) + 5.

Solve the given equation:

\[ \begin{aligned} 10x + 60 + 8x - 24 &= 25x - 20 \\ 18x + 36 &= 25x - 20 \\ 56 &= 7x, \quad x = 8 \end{aligned} \]

Now test x = 8 in the options. In 5(x - 5) = 2(x - 3) + 5, the left side is 5(3) = 15 and the right side is 2(5) + 5 = 15, so it holds.

The others fail: 5(5) = 25 but 8 + 5 = 13; 3(19) = 57 but 2(8) + 1 = 17; 2(11) = 22 but 5(3) + 4 = 19.

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