Question

greg wrote in his math journal that 17 - x = 9 is an example of an algebraic equation. which statement is true about the example greg wrote in his math journal?
gregs example is an equation because x can represent any value.
gregs example is an equation because it is a number sentence stating two amounts are equivalent.
gregs example is an equation because there are two numbers present.
gregs example is an equation because there is a variable present.

Explanation:

Step1: Recall the definition of an algebraic equation

An algebraic equation is a number sentence stating two amounts are equivalent. It has an equal sign.

Step2: Analyze each option

• Option 1: Just because \(x\) can represent any value doesn't make it an equation. An equation needs the equality statement.
• Option 2: \(17 - x=9\) is a number sentence (has numbers and operations) and states \(17 - x\) (one amount) is equivalent to \(9\) (another amount) due to the equal sign.
• Option 3: Having two numbers is not the defining characteristic of an equation. The equal sign and equivalence are.
• Option 4: Having a variable is a characteristic of an algebraic expression (e.g., \(17 - x\)) but an equation needs the equality.

Answer:

Greg's example is an equation because it is a number sentence stating two amounts are equivalent.