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Chapter 1: Problem 76

Identify each as an expression or an equation. \(8 y-(3 y+5)\)

Short Answer

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Expression

Step by step solution

01

- Understand Expressions and Equations

An expression consists of numbers, variables, and operations but does not have an equal sign. An equation has two expressions set equal to each other with an equal sign.
02

- Analyze the Given Problem

Examine the given problem: \(8y-(3y+5)\). Notice it does not contain an equal sign. It consists of variables (y), numbers, and operations (subtraction).
03

- Classify the Problem

Since \(8y-(3y+5)\) does not include an equal sign, it corresponds to an expression, not an equation.

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Key Concepts

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

expressions
An algebraic expression is a mathematical phrase that includes numbers, variables, and operations (like addition, subtraction, multiplication, and division). However, an expression *does not* have an equal sign. For example, in the expression \(8y - (3y + 5)\),
  • '8y' and '3y + 5' are terms in the expression.
  • 'y' is a variable.
  • '8', '3', and '5' are constants.
  • '-' and '+' are operations.
By combining these elements, we form an algebraic expression. It's important to remember that you cannot solve an expression in the same way you would solve an equation. Instead, you only simplify or evaluate expressions by performing operations within them.
equations
An equation, on the other hand, is like an expression but with a crucial difference: it includes an equal sign (=). This sign shows that two expressions are equal to each other. For instance, an equation might look like \(8y - (3y + 5) = 10\). Here, there's an equal sign separating the left-hand expression from the right-hand expression. In an equation, you can solve for the unknown variable by performing operations to isolate the variable on one side of the equal sign.
  • Identify the variable you want to solve.
  • Use inverse operations to isolate the variable.
  • Simplify both sides of the equation as needed.
Solving equations is a fundamental skill in algebra, as it allows you to find the value of the unknown variable that makes the equation true.
variables
Variables are symbols, usually letters like x, y, or z, that represent unknown or changeable values within expressions or equations. In the expression \(8y - (3y + 5)\):
  • 'y' is the variable.
Variables are placeholders for numbers we do not know yet. They allow us to write formulas and equations that can describe a wide range of possible situations. When dealing with variables:
  • Understand that variables can take on different values.
  • Use algebraic methods to manipulate variables.
  • Replace variables with known values to evaluate expressions.
Understanding variables is key to solving algebra problems correctly, whether simplifying expressions or solving equations.

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Most popular questions from this chapter

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(5,\) subtracted from the sum of 14 and eight times the number

Simplify each expression. $$ 6-3 z-2 z-5+z-3 z $$

Write a numerical expression for each phrase and simplify. Twice the product of \(-8\) and \(2,\) subtracted from \(-1\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (5 x-2 y)(-2 a) $$

The top of Mt. Whitney, visible from Death Valley, has an altitude of \(14,494\) ft above sea level. The bottom of Death Valley is 282 ft below sea level. Using 0 as sea level, find the difference between these two elevations.
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