Question

One less than a number is greater than the product of 3 and the difference of 5 and the number. Write and solve your inequality.

A) x - 1 > 3(5 - x)
B) x - 1 < 3(5 - x)
C) x - 1 ≥ 3(5 - x)
D) x - 1 ≤ 3(5 - x)

Answer 1

The inequality translating the statement is 'x - 1 > 3(5 - x)'. To solve it, you distribute the 3, add 3x to both sides, add 1 to both sides, and finally divide by 4 to get 'x > 4'. Option A is correct.

Step-by-step explanation:

The question asks us to write and solve an inequality involving one less than a number and the product of 3 and the difference between 5 and the number. Starting with the inequality 'One less than a number is greater than the product of 3 and the difference of 5 and the number', we can translate this into the algebraic inequality:

x - 1 > 3(5 - x)

Now let's solve the inequality step-by-step:

1. Distribute the 3 on the right side: x - 1 > 15 - 3x
2. Add 3x to both sides: 4x - 1 > 15
3. Add 1 to both sides: 4x > 16
4. Divide both sides by 4: x > 4

So the solution to the inequality is x > 4. The correct option in this case is A) x - 1 > 3(5 - x).