Write an inequality for the statement: the difference between four times a number and fourteen is at most 10.
A. [tex]$4 x-14 \geq 10$[/tex]
B. [tex]$4 x-14 \leq 10$[/tex]
C. [tex]$4(x-14) \leq 10$[/tex]
D. [tex]$4(x-14) \geq 10$[/tex]
Answer (1)
Represent the unknown number with a variable: x .
Translate 'four times a number' to 4 x .
Express 'the difference between four times a number and fourteen' as 4 x − 14 .
Translate 'is at most 10' to ≤ 10 , resulting in the inequality 4 x − 14 ≤ 10 .
Explanation
Understanding the Statement Let's break down the given statement to form the correct inequality. The statement is: 'the difference between four times a number and fourteen is at most 10.'
Defining the Variable Let's use x to represent the unknown number.
Translating 'Four times a number' 'Four times a number' translates to 4 x .
Translating 'The difference' 'The difference between four times a number and fourteen' translates to 4 x − 14 .
Translating 'Is at most 10' 'Is at most 10' means the expression is less than or equal to 10, which is written as ≤ 10 .
Forming the Inequality Combining these parts, the inequality is 4 x − 14 ≤ 10 .
Final Answer Therefore, the correct inequality is 4 x − 14 ≤ 10 .
Examples
Imagine you're trying to figure out how many hours you can work this week. You need to save $14 for a concert ticket, and you want to have at most $10 left over for fun. If you earn $4 per hour, the inequality 4 x − 14 ≤ 10 helps you determine the maximum number of hours ( x ) you can work to meet your goals. This type of problem is useful in budgeting, resource allocation, and setting limits in various real-life situations.
