Video: Determining the Domain over Which a Given Linear Function Is Either Positive or Negative

For which values of 𝑥 is the function 𝑓(𝑥) = 8𝑥 − 13 positive?

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Video Transcript

For which values of 𝑥 is the function 𝑓 of 𝑥 equals eight 𝑥 minus 13 positive?

In order to answer this question, we need to solve the inequality 𝑓 of 𝑥 is greater than zero. This is a linear inequality eight 𝑥 minus 13 is greater than zero and can be solved in much the same way as a linear equation.

The first step is to add 13 to both sides of the inequality. This gives eight 𝑥 is greater than 13. The next step is to divide both sides of the inequality by eight. This gives 𝑥 is greater than 13 over eight. As we divided by a positive number, the direction of the inequality is unchanged.

If you were answering a similar question where you were dividing by a negative number, remember you’d need to reverse the direction of the inequality when you did so.

The values of 𝑥 for which the function 𝑓 of 𝑥 is positive are values of 𝑥 which are greater than 13 over eight.

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