Question

equations always have equal signs.
an equation doesn’t contain any expressions.
this is an expression: 2x - y.
this is an equation: a = b.

Explanation:

To determine the correct statements, we analyze each one:

1. "Equations always have equal signs."

By definition, an equation is a mathematical statement that shows two expressions are equal, so it must contain an equal sign. This is true.

1. "An equation doesn’t contain any expressions."

An equation is made of two expressions (on either side of the equal sign). For example, \( a = b \) has expressions \( a \) and \( b \). Thus, this is false.

1. "This is an expression: \( 2x - y \)."

An expression is a combination of numbers, variables, and operations (without an equal sign). \( 2x - y \) fits this definition. This is true.

1. "This is an equation: \( a = b \)."

An equation requires an equal sign to show two expressions are equal. \( a = b \) has an equal sign and two expressions (\( a \) and \( b \)), so it is an equation. This is true.

Final Answer (True/False for each statement):

1. True
2. False
3. True
4. True

Answer:

To determine the correct statements, we analyze each one:

1. "Equations always have equal signs."

By definition, an equation is a mathematical statement that shows two expressions are equal, so it must contain an equal sign. This is true.

1. "An equation doesn’t contain any expressions."

An equation is made of two expressions (on either side of the equal sign). For example, \( a = b \) has expressions \( a \) and \( b \). Thus, this is false.

1. "This is an expression: \( 2x - y \)."

An expression is a combination of numbers, variables, and operations (without an equal sign). \( 2x - y \) fits this definition. This is true.

1. "This is an equation: \( a = b \)."

An equation requires an equal sign to show two expressions are equal. \( a = b \) has an equal sign and two expressions (\( a \) and \( b \)), so it is an equation. This is true.

Final Answer (True/False for each statement):

1. True
2. False
3. True
4. True