To solve the inequality \( 17 \leq -2m - 3 \), we will follow these steps:
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Isolate the term with the variable: We want to get \( -2m \) by itself on one side of the inequality. We can do this by adding 3 to both sides.
\[ 17 + 3 \leq -2m \]
Simplifying this gives:
\[ 20 \leq -2m \]
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Divide by \(-2\): Now, we need to isolate \( m \). When we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign. So we divide both sides by \(-2\):
\[ \frac{20}{-2} \geq m \]
This simplifies to:
\[ -10 \geq m \]
or, by flipping it around,
\[ m \leq -10 \]
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Conclusion: The solution to the inequality is:
\[ m \leq -10 \]
This means that any value of \( m \) that is less than or equal to \(-10\) satisfies the original inequality.
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