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Chapter 1: Problem 18

Use mathematical symbols to translate each phrase. Three more than twice a number

Short Answer

Expert verified
The expression is \( 2x + 3 \).

Step by step solution

01

- Identify the unknown

Let's denote the unknown number by a variable. We'll use the variable 'x' to represent the number.
02

- Translate 'twice a number'

The phrase 'twice a number' means two times the number. In mathematical terms, this is written as \( 2x \).
03

- Add three to 'twice a number'

The phrase 'three more than' indicates that we need to add 3 to our expression. Since we have 'twice a number' as \( 2x \), we add 3 to it. This gives us the expression \( 2x + 3 \).

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Key Concepts

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

unknown variable
In algebra, an unknown variable is like a mystery number that you need to find. Think of it as a placeholder for a number we don't know yet. We often use letters like 'x', 'y', or 'z' for these variables.
You can imagine a variable as a box that can hold any number. In the given exercise, we used 'x' to stand in for an unknown number.

To identify an unknown variable:
  • Read through the problem carefully.
  • Choose a letter to represent the unknown value. This letter will be your variable.
  • For example, if the problem talks about 'a number', you can simply use 'x' for that number.
By using variables, we're able to turn words and phrases into mathematical expressions, making problems easier to work with.
multiplication in algebra
Multiplication in algebra means combining a number with a variable or another number. This is done by multiplying them together.
Let's go back to the problem. The phrase 'twice a number' means two times that unknown number. If our unknown number is 'x', then 'twice a number' is written as \(2x\).
Here are a few important points about multiplication in algebra:
  • When you multiply a number by a variable, you write them next to each other (e.g., \(2x\)).
  • If you see no sign between a number and a variable, it means multiplication (e.g., \(2x\) means \(2\times x\)).
Using these simple rules allows us to convert verbal statements into math expressions efficiently.
addition in algebra
Addition in algebra works much like addition in arithmetic, but it involves variables and numbers. When you add, you're combining quantities together.
In our exercise, the phrase 'three more than twice a number' means we need to add 3 to \(2x\), which is 'twice a number'. So, the final expression becomes \(2x + 3\).
Important tips for addition in algebra:
  • Identify the part of the expression that represents addition (in our case, 'more than' signals addition).
  • Combine the expressions by placing a plus sign '+' between them.
  • For example, if you have \(2x\) and you add 3, you write it as \(2x + 3\).
Addition helps us build more complex expressions and solve more interesting problems.

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Most popular questions from this chapter

Jasmine is paid \(\$ 500\) per week plus \(10 \%\) of all sales she makes. a) Let \(x\) represent the amount of Jasmine's weekly sales, in dollars, and \(y\) her weekly paycheck. Write an equation expressing \(y\) in terms of \(x\) b) One week, Jasmine earned \(\$ 900 .\) What were her sales that week?

Divide. $$ \left(-\frac{2}{7}\right) \div(-1) $$

Write an equivalent expression using the distributive law. $$ 3(a+5) $$

Use roster notation to write each set. The set of all natural numbers that are multiples of 5

Use set-builder notation to write each set. \(\\{24,26,28,30,32\\}\)
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