Question

select the statements that are false.
equations always have operators.
expressions never have operators.
this is an expression: 2x = y.
this is an equation: 3a - b = 0.

Explanation:

To solve this, we analyze each statement:

Statement 1: "Equations always have operators."

An equation is a statement that two expressions are equal (e.g., \( 2 + 3 = 5 \), \( x = 4 \)). Equations involve operations (like \( +, -, = \), etc.), so this is true.

Statement 2: "Expressions never have operators."

An expression is a combination of numbers, variables, and operators (e.g., \( 2x + 3 \), \( 5 - y \)). Expressions require operators to combine terms, so this is false.

Statement 3: "This is an expression: \( 2x = y \)."

An expression does not contain an equality sign (\( = \)); it is just a combination of terms. \( 2x = y \) has an \( = \) sign, so it is an equation, not an expression. Thus, this statement is false.

Statement 4: "This is an equation: \( 3a - b = 0 \)."

An equation is a statement of equality between two expressions. \( 3a - b = 0 \) has an \( = \) sign, so it is an equation. This is true.

False Statements:

• Expressions never have operators.
• This is an expression: \( 2x = y \).

(In the format for multiple-choice-like identification, these correspond to the second and third statements.)

Answer:

To solve this, we analyze each statement:

Statement 1: "Equations always have operators."

An equation is a statement that two expressions are equal (e.g., \( 2 + 3 = 5 \), \( x = 4 \)). Equations involve operations (like \( +, -, = \), etc.), so this is true.

Statement 2: "Expressions never have operators."

An expression is a combination of numbers, variables, and operators (e.g., \( 2x + 3 \), \( 5 - y \)). Expressions require operators to combine terms, so this is false.

Statement 3: "This is an expression: \( 2x = y \)."

An expression does not contain an equality sign (\( = \)); it is just a combination of terms. \( 2x = y \) has an \( = \) sign, so it is an equation, not an expression. Thus, this statement is false.

Statement 4: "This is an equation: \( 3a - b = 0 \)."

An equation is a statement of equality between two expressions. \( 3a - b = 0 \) has an \( = \) sign, so it is an equation. This is true.

False Statements:

• Expressions never have operators.
• This is an expression: \( 2x = y \).

(In the format for multiple-choice-like identification, these correspond to the second and third statements.)