Problem 29 - Fundamentals of Mathematics

Question

Translate each phrase or sentence to a mathematical expression or equation. Four times a number minus twenty-nine is eleven.

Step-by-Step Solution

Answer

The equation is \( 4x - 29 = 11 \).

Step 1: Identify the Variable

First, we need to choose a variable to represent the unknown number. Let's use \( x \) to represent the number.

Step 2: Translate 'Four times a number'

The phrase 'four times a number' translates to an expression where the number (\( x \)) is multiplied by 4. This gives us the mathematical expression \( 4x \).

Step 3: Incorporate 'minus twenty-nine'

The phrase continues with 'minus twenty-nine', meaning we need to subtract 29 from our expression. So, we modify \( 4x \) to become \( 4x - 29 \).

Step 4: Translate 'is eleven' into an Equation

The word 'is' indicates equality, so the statement 'is eleven' translates to '= 11'. Combining this with our previous expression, we have the equation \( 4x - 29 = 11 \).

Key Concepts

Understanding Equations

An equation is a mathematical statement expressing that two things are equal. It consists of two expressions separated by an equals sign, '='. In the world of math, equations act like a balance scale. For example, in the equation \( 4x - 29 = 11 \), the idea is to find a value for \( x \) such that when you perform the operations on the left side, it equals the right side.

This balance between the two sides of an equation is crucial. It allows us to solve for unknown variables, making equations a powerful tool in mathematics. By figuring out what makes both sides equal, we ultimately solve the puzzle of the equation.

Equations can model all kinds of relationships, not only in math but also in real-life situations. By translating words into equations, we can use calculated math to find solutions in everyday situations.

Translation of Phrases to Expressions

Translating phrases into mathematical expressions is an essential skill in math. By understanding this, you can convert real-world problems into solvable mathematical language.

Let's break down the given phrase: 'Four times a number minus twenty-nine is eleven'. When translated to a mathematical expression, every word has a mathematical meaning.

• 'Four times a number' means you multiply a variable \( x \) by 4, resulting in \( 4x \).
• 'Minus twenty-nine' instructs us to subtract 29 from that product, turning \( 4x \) into \( 4x - 29 \).
• The word 'is' translates to an equal sign, '='. It signals that what comes before it is equivalent to what follows.
• 'Eleven' is the constant number the expression equals, making the equation \( 4x - 29 = 11 \).

These translations allow for a deeper understanding of how to convert real-world language into a mathematical framework.

Effective Step by Step Solutions

Approaching problems with a step-by-step method helps to break down complex tasks into manageable parts. This systematic approach simplifies the process of solving any problem, especially in math.

Breaking the phrase 'Four times a number minus twenty-nine is eleven' into steps, we follow a simple path:

• Step 1: Identify and define the variable. Here, \( x \) is the unknown number.
• Step 2: Translate components of the phrase into math language. 'Four times a number' translates to \( 4x \).
• Step 3: Adjust your expressions as the phrase continues. Subtract 29 to form \( 4x - 29 \).
• Step 4: Form complete expressions or equations. Translate 'is eleven' into '\( = 11 \)', leading to \( 4x - 29 = 11 \).

This approach not only clarifies the problem but also ensures no part of the phrase is lost in translation. It gives a structured path to reach solutions efficiently.