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: 16 < 8 * x Solution: x > 2
Practice makes perfect
We are given a verbal expression and we want to write an inequality that it represents.
Sixteen is less than eight times a number.
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 <.
Sixteen < eight times a number.
On the right-hand side of the inequality symbol we have one key phrase: times. These words tell us the operations that will be used in our inequality. Times indicates multiplication. To the left of this phrase, we have eight, which we can write as 8. To the right of the phrase we have a number, which we can write as a variable x.
eight times a number.
8 * x
On the right-hand side of the inequality symbol we have a constant.: Sixteen. We can replace it with the number 16.
Putting these sides together, we have a complete inequality.
Sixteen is less than eight times a number.
16 < 8 * x
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.
