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Determine the solution set of nine 𝑥 plus five is greater than or equal to negative four given that 𝑥 is an integer.
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The integer values are all positive and negative whole numbers.
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In order to solve our inequality, we will use the balancing method and our knowledge of inverse operations.
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The solution set will be all integers that satisfy this.
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We begin by subtracting five from both sides of the inequality.
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Negative four minus five is equal to negative nine.
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Therefore, nine 𝑥 is greater than or equal to negative nine.
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We then divide both sides by nine.
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Nine 𝑥 divided by nine is equal to 𝑥, and negative nine divided by nine is negative one.
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Therefore, 𝑥 is greater than or equal to negative one.
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As we want the solution set, we need to write our answer using set notation.
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𝑥 could be any of the following integers: negative one, zero, one, two, and so on.
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Any whole number greater than or equal to negative one would satisfy the inequality.