Eight less than four times a number is less than 56. What are the possible values of that number?

x > 12
x < 12
x < 16
x > 16

Represent the unknown number as x .
Translate the problem into the inequality 4 x − 8 < 56 .
Solve the inequality by adding 8 to both sides and then dividing by 4, resulting in x < 16 .
The possible values of the number are all numbers less than 16: x < 16 ​ .

Explanation

Understanding the Problem Let's break down the problem step by step to find the possible values of the number.

Translating to an Inequality Let the number be represented by the variable x . The problem states that 'eight less than four times a number is less than 56'. We can translate this into an inequality.

Setting up the Inequality Four times the number is 4 x . Eight less than four times the number is 4 x − 8 . So, the inequality is: 4 x − 8 < 56

Isolating the Variable Now, let's solve the inequality for x . First, we add 8 to both sides of the inequality: 4 x − 8 + 8 < 56 + 8 4 x < 64

Solving for x Next, we divide both sides of the inequality by 4: 4 4 x ​ < 4 64 ​ x < 16

Final Answer Therefore, the possible values of the number x are all numbers less than 16.


Examples
Imagine you're managing a budget for a school event. You have a maximum of $56 to spend on snacks. Each snack costs $4, but you also have a fixed cost of $8 for renting a table. This problem helps you determine how many snacks you can buy while staying within your budget. Understanding inequalities can help you make informed decisions in various real-life scenarios, such as managing expenses, planning projects, or setting limits.

Answered by GinnyAnswer | 2025-07-08

The inequality derived from the problem is x < 16 , meaning that the possible values of the number are all numbers less than 16.
;

Answered by Anonymous | 2025-08-24