The phrase is less than divides the sentence into what should be on the left-hand side and what should be on the right-hand side of the inequality.
inequality: 5 * x < -45 Solution: x < -9
Practice makes perfect
We are given a verbal expression and we want to write an inequality that it represents.
Five times a number is less than -45
Every inequality has an inequality symbol and values or expressions on either side of this symbol. In this exercise, we have the phrase is less than, so we can identify that the inequality symbol should be <.
Five times a number < -45
On the left-hand side, we have one key phrase: times. These words tell us the operations that will be used in our inequality. Times indicates multiplication. On the left-hand side of this phrase we have a word Five, so we can replace it with a number 5. On the right hand-side we have a number, which we replace with any variable. Let's use x for this purpose.
Five times a number
5 * x
On the right-hand side of the inequality symbol we have a constant. Putting these sides together, we have a complete inequality.
Five times a number is less than -45
5 * x < -45
Finally, we want to solve this inequality. Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when we divide or multiply by a negative number, we must reverse the inequality sign.
