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.