Question

ilding inequalities to solve real - world problems: tutorial
213 - 3x < 51

• 3x < 51 - 213 subtract 213 from both sides.
• 3x < - 162

x > \frac{-162}{-3} divide both sides by - 3, and flip the inequality sign.
x > 54

part e
did you have to flip the inequality sign? explain why or why not.
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Explanation:

To solve the inequality \(213 - 3x < 51\), we first subtract 213 from both sides, resulting in \(-3x < -162\). Then, we divide both sides by \(-3\). The rule for solving inequalities states that when we divide (or multiply) both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. Since we divided by \(-3\) (a negative number), we had to flip the inequality sign from \(<\) to \(>\) to maintain the truth of the inequality.

Answer:

Yes, the inequality sign had to be flipped. This is because when solving the inequality \(213 - 3x < 51\), after subtracting 213 from both sides to get \(-3x < -162\), we divided both sides by \(-3\) (a negative number). The rule for inequalities is that when you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed to keep the inequality true. So, we flipped the \(<\) to \(>\) when dividing by \(-3\).