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Chapter 1: Problem 75

Identify each as an expression or an equation. \(3 x+2(x-4)\)

Short Answer

Expert verified
Expression

Step by step solution

01

Identify Presence of Equal Sign

Check if the mathematical statement has an equal sign (=). An equation contains an equal sign, whereas an expression does not.
02

Analyze the Given Statement

Look at the provided mathematical statement: \(3x + 2(x-4)\). Notice that there is no equal sign in this statement.
03

Conclude the Type

Since there is no equal sign, the given statement \(3x + 2(x-4)\) is an expression.

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Key Concepts

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

identifying expressions
Expressions are mathematical phrases that combine numbers, variables, and operation symbols, but they do not contain an equal sign.
An example of an expression is: \(3x + 2(x-4)\).
To identify an expression, follow these simple steps:
  • Look for mathematical components like addition, subtraction, multiplication, or division.
  • Check if the statement lacks an equal sign.
  • If there is no equal sign present, then it is an expression.
Expressions can be simplified but cannot be solved for a specific value, unlike equations. They represent a value that might change if variables within them change.
identifying equations
An equation is a mathematical statement that shows the equality of two expressions by using an equal sign.
For example, in the equation \(3x + 2(x-4) = 10\), the left and right sides are claimed to be equal.
To identify an equation, follow these steps:
  • Look for an equal sign (=) within the statement.
  • Ensure the parts on both sides of the equal sign can be evaluated to check for equality.
  • If the statement includes an equal sign, it is an equation.
Equations can often be solved to find the value of variables that satisfy the equality.
equal sign in equations
The equal sign (=) plays a crucial role in equations. It indicates that the value on the left side of the sign is equivalent to the value on the right side.
Understanding the equal sign helps differentiate between expressions and equations.
Here's why the equal sign is important in equations:
  • It shows balance or equality, meaning both sides have the same value.
  • Its presence allows us to solve equations by performing operations that maintain equality.
Without an equal sign, you cannot set the statement for solving; it remains an expression. Recognizing the equal sign is your first step in identifying 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. Six times a number added to \(-4,\) subtracted from twice the sum of three times the number and 4 (Hint: Twice means two times.)

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

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 3 is \(-3\)

The surface, or rim, of a canyon is at altitude 0. On a hike down into the canyon, a party of hikers stops for a rest at \(130 \mathrm{m}\) below the surface. The hikers then descend another \(54 \mathrm{m} .\) Write the new altitude as a signed number.

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \frac{2 y^{2}-x}{a+10} $$
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