Exercise 5 Page 467

We are asked to write an indirect proof of the following claim. Given:&5x+7≥ 52 Prove:&x≥ 9 To do so, let's follow the three step process of an indirect proof.

Step 1

First, we should assume that the claim is false. Assume:x < 9

Step 2

Next, we need to look for some consequences of our assumption. We can do this by trying to match the left-hand side of our inequality with the left-hand side of the given inequality. We will use the Properties of Inequality to do this.

If x<9, then 5x+7<52. This, however contradicts the given statement: 5x+7≥ 52.

Step 3

Since our assumption lead to a contradiction, we know that our assumption cannot be true. Since x cannot be less than 9, we proved that x≥ 9.