To solve the inequality \( 19(m - 2) - 18 > 20 \), we will first simplify and solve for \( m \).
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Start by distributing \( 19 \) in the expression: \[ 19m - 38 - 18 > 20 \]
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Combine like terms: \[ 19m - 56 > 20 \]
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Add \( 56 \) to both sides: \[ 19m > 76 \]
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Divide both sides by \( 19 \): \[ m > 4 \]
Now we have the solution to the inequality: \( m > 4 \).
Graphing the solution:
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Identify the endpoint, which is \( 4 \).
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Since the solution is \( m > 4 \), we will use an open circle at \( 4 \) (indicating that \( 4 \) is not included in the solution).
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Draw a ray extending to the right of \( 4 \) to represent all values greater than \( 4 \).
Summary of the graph:
- Open circle at \( 4 \)
- Ray starting just after \( 4 \) and continuing infinitely to the right.
Thus, the graphical representation of the solution \( m > 4 \) has the open circle and the ray extending to the right from \( 4 \).