Question

Two is greater than the sum of 3 and one-fourth of a number. What’s the inequality and the solution to the inequality?

a) 2 > 3 + 0.25x
b) 2 < 3 + 0.25x
c) 2 ≥ 3 + 0.25x
d) 2 ≤ 3 + 0.25x

Answer 1

To solve the inequality 2 > 3 + 0.25x, subtract 3 from both sides to get -1 > 0.25x. Then, divide both sides by 0.25 to obtain -4 > x. Hence, the solution is x < -4.

Step-by-step explanation:

To solve the inequality, let's translate the given statement into mathematical symbols. We are told that 'Two is greater than the sum of 3 and one-fourth of a number.' Let's call the number x. So the inequality becomes: 2 > 3 + 0.25x.

To solve this inequality, we need to isolate the variable x. We can start by subtracting 3 from both sides: 2 - 3 > 3 + 0.25x - 3, which simplifies to -1 > 0.25x.

Next, we can divide both sides by 0.25 to get: -4 > x. Rearranging the inequality, we have x < -4.

Therefore, the inequality is 2 > 3 + 0.25x and the solution to the inequality is x < -4.