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Chapter 3: Problem 2

Identify each as an expression or an equation. $$\frac{3}{4} k+5(k-6)=2$$

Short Answer

Expert verified
The given statement is an equation, as it has an equal sign comparing two expressions and can be solved for the variable k. The equation is: \[ \frac{3}{4}k + 5(k-6) = 2 \]

Step by step solution

01

Analyze the given statement

The given statement is: \[ \frac{3}{4}k + 5(k-6) = 2 \] We can see that there is an equal sign present in the statement, meaning it compares two different expressions.
02

Identify the nature of the statement

As there is an equal sign, which separates the statement into two parts, we can conclude that this statement is an equation. It can be solved for the variable k. So the given mathematical statement is an equation.

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Key Concepts

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

Expressions
An expression is a key concept in mathematics that allows us to represent quantities and perform operations. Expressions consist of numbers, variables, and operation signs like addition or multiplication. There are no equal signs in expressions. Instead, they are often used to describe a value or relate different quantities.
For example, if you see something like \(3x + 5\), that's an expression.
  • Expressions don't have solutions because they're not equations. They represent a value or simplify to a single number.
  • This makes expressions very important for simplifying complex algebraic problems.
  • Understanding expressions is the first step before diving into equations.
By recognizing expressions, you can more easily identify what parts are variables and how they interact. This becomes crucial when you later start solving equations.
Solving Equations
Solving equations involves finding the value of the variable that makes the equation true. An equation is a mathematical statement formed by setting two expressions equal to each other, often including letters that stand for unknown numbers, called variables.
For example, in the equation \(3x + 5 = 11\), you want to find the value of \(x\) that satisfies this equation.
  • To solve equations, you need to perform operations that simplify the expression on both sides.
  • Common techniques include isolating the variable, using inverse operations, and maintaining balance by performing the same actions on both sides of the equation.
  • An equation can be simple like linear equations or more complex like quadratic or polynomial equations.
Understanding the steps to solve equations builds the foundation for tackling more sophisticated mathematical problems.
Variable Identification
Variables are symbols used in mathematics to represent unknowns or changing values. They are the placeholders for the numbers you need to find or work with. Typically, mathematicians use letters such as \(k\), \(x\), or \(y\) as variables.
Identifying variables is crucial when interpreting or solving mathematical problems like equations and expressions.
  • In an equation, the variable is the unknown we aim to discover.
  • Identifying variables involves recognizing which symbols act as placeholders for values that haven't been solved yet.
  • In the exercise \(\frac{3}{4} k + 5(k-6) = 2\), \(k\) is the variable.

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Most popular questions from this chapter

Solve using the five "Steps for Solving Applied Problems." See Examples \(7-9\) Nine less than a number is eleven. Find the number.

Solve each equation by first clearing fractions or decimals. $$\frac{1}{2}=\frac{2}{9}(3 x-2)-\frac{x}{9}-\frac{x}{6}$$

Solve using the five "Steps for Solving Applied Problems." See Examples \(7-9\) One-third of a number increased by four is one. Find the number.

Solve each formula for the indicated variable. $$f=\frac{R}{2}\( for \)R$ (physics)$$

Solve each formula for the indicated variable. $$U=\frac{1}{2} L I^{2}\( for \)L$ (physics)$$
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