Problem 70 - Algebra for College Students

Question

Give, in interval notation, the unknown numbers in each description. If 8 is subtracted from a number, then the result is at least \(5 .\)

Step-by-Step Solution

Answer

[13, \infty)

Step 1: Define the variable

Let the unknown number be denoted by the variable, say, \(x\).

Step 2: Transform the word problem into an inequality

According to the problem, if 8 is subtracted from \(x\), the result is at least 5. This can be written as an inequality: \[x - 8 \geq 5\]

Step 3: Solve the inequality

To find the values of \(x\), solve the inequality: \[x - 8 \geq 5\] Add 8 to both sides of the inequality: \[x \geq 13\]

Step 4: Express the solution in interval notation

The inequality \(x \geq 13\) means that \(x\) is any number greater than or equal to 13. In interval notation, this is written as: \([13, \infty)\)

Key Concepts

Understanding Algebra

Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. In this exercise, we used a variable, denoted by \(x\), to represent an unknown number. This approach makes solving complex problems more manageable.

To solve the given problem, we transformed the word problem into an algebraic inequality. This involves interpreting the problem's language and turning it into mathematical expressions. Here, the phrase