To solve the inequality \( 2x - 6 < 7(x + 2) \), we will first expand the right-hand side and then isolate \( x \).
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Expand the right-hand side:
\[ 7(x + 2) = 7x + 14 \]
So the inequality becomes:
\[ 2x - 6 < 7x + 14 \]
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Next, let's isolate the \( x \) terms. Subtract \( 2x \) from both sides:
\[ -6 < 7x - 2x + 14 \]
This simplifies to:
\[ -6 < 5x + 14 \]
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Now, subtract 14 from both sides:
\[ -6 - 14 < 5x \]
Which simplifies to:
\[ -20 < 5x \]
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Finally, divide each side by 5:
\[ -4 < x \]
This can also be written as:
\[ x > -4 \]
So the solution to the inequality \( 2x - 6 < 7(x + 2) \) is:
\[ x > -4 \]