$\"\"$

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One third of the sum of $\"\"$ times a number and $\"\"$ is less than one fourth the sum of six times that number and $\"\"$ .

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Let $\"\"$ be the a number.

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Write an equation.

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The words one third of the sum of $\"\"$ times a number and $\"\"$ represent the expression is $\"\"$ .

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The words one fourth the sum of six times that number and $\"\"$ represent the expression is $\"\"$

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The inequality is $\"\"$ .

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Solve the inequality.

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$\"\"$ (Original inequality)

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$\"\"$ (Multiply each side by $\"\"$ )

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$\"\"$ (Cancel common factors)

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$\"\"$ (Apply distributive property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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$\"\"$

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The solution set of the inequality is $\"\"$ .