To solve the equation \(-8(5x + 15) = 7\), we will follow these steps:
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Distribute the -8 on the left side of the equation: \[ -8 \cdot 5x - 8 \cdot 15 = 7 \] This simplifies to: \[ -40x - 120 = 7 \]
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Next, we will isolate the term with \(x\) by adding 120 to both sides: \[ -40x - 120 + 120 = 7 + 120 \] This simplifies to: \[ -40x = 127 \]
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Now, divide both sides by -40 to solve for \(x\): \[ x = \frac{127}{-40} \] This can also be written as: \[ x = -\frac{127}{40} \]
Thus, the solution to the equation is: \[ x = -\frac{127}{40} \]