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Write an inequality to describe the following and then solve it.
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Negative five times a number is at least negative 45.
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We’ll start by writing the inequality.
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We’ve got negative five being multiplied by some number, which we’ll represent with the variable 𝑥, at least negative 45.
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We know the other side will have a negative 45.
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But what symbol should “at least” represent?
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We need to consider if this could be more, equal, or less.
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“At least” means it could be equal, but it could not be less.
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“At least” could also mean more.
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So it’s equal to or more than.
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And mathematically, we would represent that with a greater than or equal to symbol.
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If negative five times a number is at least negative 45, then negative five 𝑥 is greater than or equal to negative 45.
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This is the first part of the problem, but we’ll now need to try and solve for 𝑥.
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Since we’re dealing with an inequality, it should immediately be on our radar that if we’re multiplying and dividing with positive values, the sign stays the same.
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But if we’re multiplying or dividing with a negative number, we have to flip the sign.
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𝑥 is being multiplied by negative five.
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And to get 𝑥 by itself, to solve for 𝑥, we’ll need to divide both sides of the equation by negative five.
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Since we are dividing by a negative here, we must flip the inequality symbol.
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Negative five 𝑥 divided by negative five equals 𝑥.
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The sign is flipped.
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And negative 45 divided by negative five is nine.
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Negative five 𝑥 is greater than or equal to negative 45.
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And that means 𝑥 is less than or equal to nine.