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Chapter 1: Problem 1

Write each phrase as an algebraic expression. Use \(x\) as the variable unless otherwise indicated. Two less than five times a number

Short Answer

Expert verified
5x - 2

Step by step solution

01

Identify the variable

The phrase describes a variable, which we will designate as \(x\).
02

Translate 'five times a number'

'Five times a number' indicates multiplication. So, we write it as \(5x\).
03

Translate 'two less than'

'Two less than' means subtracting 2. Since it is two less than the five times the number, we place \( - 2\) after \(5x\).
04

Combine the parts

Putting it all together, the algebraic expression is \(5x - 2\).

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Key Concepts

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

Variable Identification
In algebra, a variable represents an unknown value that we are trying to find. We often use letters like \(x\) to denote variables. For example, in the phrase 'five times a number', the 'number' is our unknown value, which we will call \(x\).
Recognizing this variable is the first step in converting any written phrase into an algebraic expression. By identifying the variable, we can start translating the words into mathematical operations.
Multiplication in Algebra
In many algebraic problems, you'll come across phrases like 'five times a number鈥�. Here, 'five times' indicates multiplication. So if our variable is \(x\), 'five times \(x\)' becomes \(5x\).

When translating words into mathematics:
  • 'Twice a number' becomes \(2x\)
  • 'Three times a number' becomes \(3x\)
  • And so on.
It's crucial to understand how multiplication is represented in algebra, as it frequently appears in expressions and equations.
Subtraction in Algebra
Subtraction in algebra involves taking one quantity away from another. Phrases like 'two less than' mean we subtract 2. In our example, 'two less than five times a number' translates to \(5x - 2\).
Notice how the subtraction part comes after the multiplication. It's important to respect the order of operations in algebra.

More examples include:
  • 'Ten less than a number' becomes \(x - 10\)
  • 'Three less than twice a number' becomes \(2x - 3\)
    • .
Understanding how to perform subtraction in algebra is critical for forming correct expressions and solving equations effectively.

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Most popular questions from this chapter

In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water \(T\) (in \({ }^{\circ} \mathrm{F}\) ) can be approximated by the model \(T=-1.83 a+212,\) where \(a\) is the altitude in thousands of feet. a. Determine the temperature at which water boils at an altitude of \(4000 \mathrm{ft}\). b. Two campers hiking in Colorado boil water for tea. If the water boils at \(193^{\circ} \mathrm{F}\), approximate the altitude of the campers. Give the result to the nearest hundred feet.

Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. (See Examples \(1-3)\) $$\frac{4+x}{2}-\frac{x-3}{5}<-\frac{x}{10}$$

Seismographs can record two types of wave energy (P waves and S waves) that travel through the Earth after an earthquake. Traveling through granite, \(\mathrm{P}\) waves travel approximately \(5 \mathrm{~km} / \mathrm{sec}\) and \(\mathrm{S}\) waves travel approximately \(3 \mathrm{~km} / \mathrm{sec} .\) If a geologist working at a seismic station measures a time difference of 40 sec between an earthquake's P waves and S waves, how far from the epicenter of the earthquake is the station?

Use the model \(s=-\frac{1}{2} g t^{2}+v_{0} t+s_{0}\). NBA basketball legend Michael Jordan had a 48 -in. vertical leap. Suppose that Michael jumped from ground level with an initial velocity of \(16 \mathrm{ft} / \mathrm{sec}\). a. Write a model to express Michael's height (in \(\mathrm{ft}\) ) above ground level \(t\) seconds after leaving the ground. b. Use the model from part (a) to determine how long it would take Michael to reach his maximum height of 48 in. \((4 \mathrm{ft})\)

Write each expression in terms of \(i\) and simplify. (See Examples \(1-2)\) $$\sqrt{-100}$$
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