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Chapter 3: Problem 74

Translate the given phrase or sentence algebraically. \(a\) is at most 5

Short Answer

Expert verified
a \( \leq 5 \)

Step by step solution

01

Understand the Phrase

The phrase 'at most' implies a maximum value. It means that the variable 'a' can be equal to or less than the given value (5) but not more.
02

Write the Inequality

Since 'a' is at most 5, it translates to the inequality: \( a \leq 5 \).

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Key Concepts

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

inequalities
Inequalities are used to compare two expressions. They show the relationship between values that are not necessarily equal. In this exercise, we worked with the phrase 'at most', which implied an upper limit. The statement 'a is at most 5' suggests that 'a' can be any number up to and including 5. To represent this, we use the inequality: a \leq 5.Understanding basic inequality symbols is crucial:
  • \(<\) means 'less than'.
  • \(\leq\) means 'less than or equal to'.
  • \(>\) means 'greater than'.
  • \(\geq\) means 'greater than or equal to'.
Breaking down the phrase helps identify the correct symbol. In this example, 'at most' clearly indicates 'less than or equal to.'
algebraic expressions
Algebraic expressions are combinations of variables, numbers, and arithmetic operators. They form the basis of algebra and help in translating real-world situations into mathematical language. In the given exercise, the phrase translates into an inequality, which is also an algebraic expression.The inequality \(a \leq 5\) is an expression where:
  • 'a' is the variable.
  • '5' is the constant.
  • '\(\leq\)' is the inequality symbol connecting them.
Algebraic expressions can be complex or simple, but understanding their components is key to solving or rearranging them. Knowing how to convert phrases into algebraic expressions provides a foundation for tackling more advanced problems in algebra.
mathematical phrases
In algebra, translating mathematical phrases into algebraic symbols is a vital skill. Phrases like 'at most', 'at least', 'greater than', and 'less than' need accurate conversion to their respective symbols. This ensures the expressions correctly represent the given conditions.For example:
  • 'At most' translates to '\(\leq\)'.
  • 'At least' translates to '\(\geq\)'.
  • 'Greater than' translates to '\(>\)'.
  • 'Less than' translates to '\(<\)'.
By identifying key words and translating them correctly, you turn a phrase describing a condition into a clear algebraic inequality. The key is to break down the phrase logically. Practice with various phrases will improve your ability to quickly and accurately perform these translations.

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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. Anthropologists often extrapolate the appearance of a human being from the parts of a skeleton they uncover. The following mathematical model relates the height \(h\) (in centimeters) of the individual to the length \(f\) (in centimeters) of the femur (thigh bone): $$h=3.68 f+21.44$$ (a) Use this model to find the height of an individual whose femur measures \(35 \mathrm{cm}\) (b) Use this model to find the length of a femur corresponding to an individual who is \(180 \mathrm{cm}\) tall.

Solve each inequality. $$1 \leq 6-x<3$$

Perform the indicated operations and simplify as completely as possible. $$4(x-3 y)+2(3 x-y)$$

Translate the given phrase or sentence algebraically. 7 greater than \(x\)

A person can drive from town A to town B at a certain rate of speed in 5 hours. If he increases his speed by \(15 \mathrm{kph}\), he can make the trip in 4 hours. How far is it from town A to town B?
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