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Chapter 2: Problem 10

Translate to an inequality. A number is greater than or equal to \(4 .\)

Short Answer

Expert verified
\( x \geq 4 \)

Step by step solution

01

Identify the unknown number

Let the unknown number be represented as the variable, say \( x \).
02

Express the condition

The condition given is that the number is greater than or equal to 4.
03

Translate the condition to an inequality

The inequality representing the condition is \( x \geq 4 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It is concerned with finding the unknown values. In algebra, we use letters, often called variables, to represent these unknown values. These variables can stand for various quantities and enable us to form equations and inequalities that depict different relationships.
For example, when we say that a number is greater than or equal to 4, we use algebra to express this as an inequality. This can be done by using a variable, such as 'x', to represent the unknown number and then creating an expression that utilizes this variable.
inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They are similar to equations but instead of using an equals sign, they use inequality symbols like >, <, 鈮�, and 鈮�.
The inequality symbol < means 'less than,' > means 'greater than,' 鈮� means 'less than or equal to,' and 鈮� means 'greater than or equal to.'
In the exercise, we translated the statement 'A number is greater than or equal to 4' into an inequality using the symbol 鈮�. This represented that the unknown variable 'x' is at least 4, or possibly more.
variables
Variables are fundamental to algebra. They are symbols used to represent numbers in mathematical expressions and equations. Variables allow us to generalize problems and solve for unknown values.
In our exercise, we used the variable 'x' to represent the unknown number. When translating a statement into a mathematical expression, it is essential to identify what you do not know and choose an appropriate variable to stand in for that unknown.
By incorporating variables, we can manipulate and solve for these unknowns through algebraic methods, like creating and solving inequalities.
mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operators (like +, -, *, and /) that represent a particular value or relationship. They do not include equality or inequality symbols, which are used in equations and inequalities respectively.
In the context of our exercise, the inequality 'x 鈮� 4' is a form of mathematical expression. It combines the variable 'x' with the number 4 and uses the 'greater than or equal to' operator to express the relationship.
Translating verbal statements into mathematical expressions is a crucial skill in algebra, allowing for clear and concise representation of relationships and conditions presented in word problems.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. To remain on financial aid, Millie must complete an average of at least 7 credits per quarter each year. In the first three quarters of \(2010,\) Millie completed \(5,7,\) and 8 credits. How many credits of course work must Millie complete in the fourth quarter if she is to remain on financial aid?

Would it be better to receive a \(5 \%\) raise and then, a year later, an \(8 \%\) raise or the other way around? Why?

Use an inequality and the five-step process to solve each problem. As part of an outdoor education course, Tricia needs to make a bright-colored triangular flag with an area of at least \(3 \mathrm{ft}^{2} .\) What heights can the triangle be if the base is \(1 \frac{1}{2} \mathrm{ft} ?\) (THE IMAGE CANNOT BE COPY)

Use an inequality and the five-step process to solve each problem. As a rule of thumb, debt payments (other than mortgages) should be less than \(8 \%\) of a consumer's monthly gross income. Oliver makes \(\$ 54,000\) per year and has a \(\$ 100\) student-loan payment every month. What size car payment can he afford?

Use an inequality and the five-step process to solve each problem. On July 1, Garrett's Pond was \(25 \mathrm{ft}\) deep. since that date, the water level has dropped \(\frac{2}{3} \mathrm{ft}\) per week. For what dates will the water level not exceed \(21 \mathrm{ft} ?\)
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