Solve five 𝑥 plus seven is less than negative three. Write your answer as an interval.
In order to solve this inequality, we are going to approach it in the same way as we would an equation. Subtracting seven from both sides, using the balancing method, leaves us with five 𝑥 is less than negative 10. This is because negative three minus seven equals negative 10. If we divide both sides of this equation by five, we are left with 𝑥 is less than negative two. Negative 10 divided by five is negative two. Five 𝑥 divided by five is 𝑥.
One way of demonstrating this solution, 𝑥 is less than negative two, is on a number line. As you can see, we have circled negative two and our arrow is pointing to the left. It is also important to note that the circle is not coloured in because our solution does not include the number negative two. It is just the solution of all the values less than negative two. Had the inequality sign been less than or equal to, then we would have coloured in the circle or dot.
Our solution can be written as an interval in one of two ways. 𝑥 can take any value less than negative two down to negative infinity. Therefore, the interval can be written: negative infinity, comma, negative two.