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Chapter 3: Problem 73

Translate the given phrase or sentence algebraically. \(x\) is at least 5

Short Answer

Expert verified
\( x \geq 5 \)

Step by step solution

01

Identify the key phrase

The key phrase in the sentence is 'at least 5'. This indicates a comparison where something is greater than or equal to a certain value.
02

Determine the inequality

The phrase 'at least 5' means that the value of the variable is 5 or more. Algebraically, this is represented by the inequality symbol '鈮�'.
03

Set up the inequality

Translate the phrase directly into an inequality. Since \( x \) is at least 5, write it as \( x \geq 5 \).

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Key Concepts

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

Inequality Symbols
Inequality symbols are essential tools in algebra that help us compare values. Unlike the equal sign '=' that shows two values are the same, inequality symbols tell us if one value is larger, smaller, or simply different from another.
Inequality symbols include:
  • '>': Greater than. Example: In the expression 'x > 5', x must be more than 5.
  • '<': Less than. Example: 'y < 7' indicates y is smaller than 7.
  • '鈮�': Greater than or equal to. Example: 'x 鈮� 5' means x is at least 5.
  • '鈮�': Less than or equal to. Example: 'y 鈮� 7' shows y is at most 7.
  • '鈮�': Not equal to. Example: 'x 鈮� 4' means x is not equal to 4.
By using these symbols, we easily express conditions and constraints. In the given exercise, understanding that 'at least 5' translates to using the '鈮�' symbol is key.
Translating Phrases to Algebra
Translating words into algebraic expressions or inequalities might seem tricky at first, but it gets easier with practice. This translation involves identifying key phrases and understanding what they mean in mathematical terms.
Let's consider a similar example to the given exercise:
Suppose we have the phrase 'A number y is less than or equal to 10.' Here's how we translate it step-by-step:
  • Step 1: Identify the key phrase. Here, it's 'less than or equal to 10.'
  • Step 2: Determine the inequality. 'Less than or equal to' corresponds to the '鈮�' symbol.
  • Step 3: Translate into an algebraic inequality. Combine the variable and the inequality symbol to form 'y 鈮� 10.'
In the given exercise, 'is at least 5' identifies the key phrase, meaning that the variable x is greater than or equal to 5, which translates to 'x 鈮� 5.'
Comparison in Algebra
Comparison in algebra focuses on understanding and expressing how numbers and variables relate to each other. The exercise emphasizes how to understand phrases that compare quantities and turn them into algebraic inequalities.
Here鈥檚 a quick overview:
  • Greater than (>): Shows that one number is more than another.
  • Less than (<): Used when one number is smaller.
  • Greater than or equal to (鈮�): Indicates a number is at least something or more.
  • Less than or equal to (鈮�): Means a number is at most something.
For the given phrase 'x is at least 5,' we know that x must be greater than or equal to 5.
This tells us that any value of x can't be lower than 5. Learning to quickly identify these comparisons allows for efficient translation and accurate mathematical expressions.

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Most popular questions from this chapter

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. The width of a rectangle is 8 less than three times its length. If the perimeter of the rectangle is 24 in., find the dimensions of the rectangle.

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. A trucking company determines that the cost \(C\) (in dollars per mile) of operating a truck is given by \(C=0.003 s+0.21,\) where \(s\) is the average speed of the truck. (a) Find the cost per mile if the truck averages 55 miles per hour. (b) Find the average speed that yields a cost per mile of \(\$ 0.35\)

Set up an inequality and solve it. Be sure to clearly label what the variable represents. An organization wants to sell tickets to a concert. It plans on selling 300 reserved-seat tickets and 150 tickets at the door. The price of a reserved- seat ticket is to be \(\$ 2\) more than a ticket at the door. If the organization wants to collect at least \(\$ 3,750\), what is the minimum price it can charge for a reserved-seat ticket?

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(-x<3 ;\) divide each side by \(-1\)

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. The length of a rectangle is 12 more than four times its width. If the perimeter of the rectangle is 134 meters, find the dimensions for the rectangle.
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