Discussion

If \(5(3x + 4) - 8(6x + 7) = 9x - 8\), then what is the value of \((3x + 4)\) ?

Answer: A

The value of (3x + 4) is 2.

Expand and solve:

\[ \begin{aligned} 15x + 20 - 48x - 56 &= 9x - 8 \\ -33x - 36 &= 9x - 8 \\ -42x &= 28 \\ x &= -\tfrac{2}{3} \end{aligned} \]

\[ 3x + 4 = 3\left(-\tfrac{2}{3}\right) + 4 = 2 \]

Check: 5(2) − 8(6x + 7) = 10 − 8(3) = −14, and 9x − 8 = −6 − 8 = −14. The other values of 3x + 4 (3, 0 and 1) do not satisfy the equation.

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