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\begin{tabular}{l} Solve for \( x \) \\ \( \qquad 3 x-9+5(x+5)<0 \) \\ \hline\end{tabular}

Ask by Lang Mann. in the United States
Jan 29,2025

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Answer

\( x < -2 \)

Solution

To solve the inequality: \[ 3x - 9 + 5(x + 5) < 0 \] **Step 1: Distribute and combine like terms** \[ 3x - 9 + 5x + 25 < 0 \] \[ (3x + 5x) + (-9 + 25) < 0 \] \[ 8x + 16 < 0 \] **Step 2: Isolate \( x \)** Subtract 16 from both sides: \[ 8x < -16 \] Divide both sides by 8: \[ x < -2 \] **Solution:** \[ x < -2 \]

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Mind Expander

To solve the inequality \( 3x - 9 + 5(x + 5) < 0 \), first simplify the left side: 1. Distribute the \( 5 \): \[ 3x - 9 + 5x + 25 < 0 \] 2. Combine like terms: \[ (3x + 5x) + (-9 + 25) < 0 \implies 8x + 16 < 0 \] 3. Isolate \( x \): \[ 8x < -16 \implies x < -2 \] So the solution to the inequality is \( x < -2 \).

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