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:
p+5 < 17 Solution: p < 12
Practice makes perfect
We are given a word sentence and we want to write an inequality that it represents. What can you do to isolate a variable in an inequality?
Five more than a number p is less than 17.
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 <.
Fivemore than a numberp < 17.On the left-hand side, we have the phrase a number p. These words tell us that p is a variable symbol.
Five more thana numberp < 5.
Five more than p < 5
Next phrase on the left-hand side is Five more than. The word more indicates addition. The word Five implies that the number that should be added is 5.
Five more than p < 17.
p +5 < 17
On the right-hand side, we have the constant 17. If we put these sides together, we have a complete inequality.
Five more than a number p is less than 17.
p +5 < 17
Now let's solve this inequality. Remember that 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.
