To solve the equation \( \frac{4}{7}x + 7 = -6 \), follow these steps:
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Isolate the term with \( x \): Subtract 7 from both sides of the equation: \[ \frac{4}{7}x + 7 - 7 = -6 - 7 \] This simplifies to: \[ \frac{4}{7}x = -13 \]
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Eliminate the fraction: Multiply both sides by \( \frac{7}{4} \) to solve for \( x \): \[ x = -13 \cdot \frac{7}{4} \] This simplifies to: \[ x = -\frac{91}{4} \]
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Convert to decimal (if necessary): You can convert \( -\frac{91}{4} \) to a decimal: \[ -\frac{91}{4} = -22.75 \]
So, the solution is: \[ x = -\frac{91}{4} \quad \text{or} \quad x = -22.75 \]