Video: Writing the Solution Set of a Linear Inequality in the Set of Integers

Write the set of all integer solutions to 4𝑥 − 8 < −4.

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Video Transcript

Write the set of all integer solutions to four 𝑥 minus eight is less than negative four.

Integers are whole numbers. Therefore, we are only looking for whole number solutions, positive or negative, to the inequality.

Using the balancing method, we can add eight to both sides of the inequality. This leaves us four 𝑥 is less than negative four plus eight.

As negative four plus eight is positive four, four 𝑥 is less than four. Dividing both sides of this inequality by four leaves us with an answer of 𝑥 is less than one.

This means that 𝑥 can be any whole number value that is less than one. Therefore, the solution set or set of values that solve the inequality are zero, negative one, negative two, negative three, and all of the negative numbers.

There are an infinite number of integer solutions to the inequality four 𝑥 minus eight is less than negative four.

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