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Algebra / Linear inequalities in one or two variables Difficulty: Hard

A number $x$ is at most $2$ less than $3$ times the value of $y$ . If the value of $y$ is $negative 4$ , what is the greatest possible value of $x$ ?

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Explanation

The correct answer is $negative 14$ . It's given that a number $x$ is at most $2$ less than $3$ times the value of $y$ . Therefore, $x$ is less than or equal to $2$ less than $3$ times the value of $y$ . The expression $3 y$ represents $3$ times the value of $y$ . The expression $3 y minus 2$ represents $2$ less than $3$ times the value of $y$ . Therefore, $x$ is less than or equal to $3 y minus 2$ . This can be shown by the inequality $x \leq 3 y - 2$ . Substituting $negative 4$ for $y$ in this inequality yields $x \leq 3 (- 4) - 2$ or, $x \leq - 14$ . Therefore, if the value of $y$ is $negative 4$ , the greatest possible value of $x$ is $negative 14$ .