Question

Solve this problem by writing and solving an inequality. Five more than four times a number is less than 25. What are the possible values of the number? Show your work.

Answer 1

Let the number be x. The sentence "Five more than four times a number is less than 25" becomes the inequality
5 + 4x < 25.

Subtract 5 from both sides:
4x < 20.

Divide both sides by 4 (positive, so the inequality direction stays the same):
x < 5.

So the possible values are all numbers less than 5 (interval notation: (-∞, 5)). For example, 4, 0, and -2 all work; 5 does not because it makes the left side equal to 25.