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How are the solutions to the inequality -3x >= 18 different from the solutions to -3x > 18 ? Explain your reasoning.

How are the solutions to the inequality $-3x \geq 18$ different from the solutions to -3x > 18 ? Explain your reasoning.

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Find values of derivatives using limits

Full solution

Q. How are the solutions to the inequality

-3x \geq 18

different from the solutions to

-3x > 18

? Explain your reasoning.

Solve Inequality $-3x \geq 18$ : Step $1$ : Solve the inequality $-3x \geq 18$ . $\newline$ Divide both sides by $-3$ , remembering to flip the inequality sign because we are dividing by a negative number. $\newline$ $-3x \geq 18$ becomes $x \leq -6$ .
Solve Inequality -3x > 18: Step $2$ : Solve the inequality -3x > 18. Similarly, divide both sides by $-3$ and flip the inequality sign. -3x > 18 becomes x < -6.
Compare Solutions: Step $3$ : Compare the solutions of $x \leq -6$ and x < -6. The solution $x \leq -6$ includes $x = -6$ and all numbers less than $-6$ . The solution x < -6 includes only numbers less than $-6$ , not including $-6$ itself.

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