Problem 50
Question
Translate to an algebraic expression. Twenty less than six times a number
Step-by-Step Solution
Verified Answer
6x - 20
1Step 1: Identify the unknown number
Let the unknown number be represented by the variable, say, \( x \).
2Step 2: Translate 'six times a number'
The phrase 'six times a number' translates to the algebraic expression \( 6x \).
3Step 3: Translate 'twenty less than'
The phrase 'twenty less than' indicates a subtraction, meaning you subtract 20 from the expression formed in Step 2.
4Step 4: Form the final algebraic expression
Combine the results from the previous steps. Subtract 20 from \( 6x \), giving the final algebraic expression: \( 6x - 20 \).
Key Concepts
algebraic expressionvariables in algebrasubtraction in algebra
algebraic expression
An algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols. It's like a sentence in math. For instance, in the original exercise, we translate a word problem into an algebraic expression. This helps us manage and solve problems more systematically.
Algebraic expressions can consist of:
Understanding algebraic expressions is important as it paves the way for solving equations and modeling real-world scenarios.
Algebraic expressions can consist of:
- Variables (like x or y)
- Constants (specific numbers like 1, 2, or 3)
- Operations (such as addition, subtraction, multiplication, division)
Understanding algebraic expressions is important as it paves the way for solving equations and modeling real-world scenarios.
variables in algebra
In algebra, variables are symbols used to represent unknown numbers or values. They are often letters like x, y, or z. In the given exercise, we used the variable x to stand for the unknown number.
Variables help us generalize mathematical problems and solutions. They are placeholders that can take on different values depending on the problem's requirements. For instance, in our example, 'six times a number' is translated to '6x', where x is the variable representing the unknown number.
When working with variables:
Variables help us generalize mathematical problems and solutions. They are placeholders that can take on different values depending on the problem's requirements. For instance, in our example, 'six times a number' is translated to '6x', where x is the variable representing the unknown number.
When working with variables:
- Remember they can represent any number.
- Think of them as a way to simplify and solve problems.
- Use them to form algebraic expressions and equations.
subtraction in algebra
Subtraction in algebra works similarly to subtraction in basic arithmetic; it involves taking away one quantity from another. However, in algebra, these quantities can be variables, constants, or a mix of both.
In our exercise, we translated the phrase 'twenty less than six times a number'. Here, subtraction is indicated by 'less than', telling us to subtract 20 from 'six times a number'. Hence, we get the expression '6x - 20'.
When performing subtraction in algebra:
In our exercise, we translated the phrase 'twenty less than six times a number'. Here, subtraction is indicated by 'less than', telling us to subtract 20 from 'six times a number'. Hence, we get the expression '6x - 20'.
When performing subtraction in algebra:
- Identify the terms to subtract.
- Ensure the correct order; 'less than' usually means reversing the terms.
- Simplify the expression by combining like terms if any.