Understanding Algebraic Expressions and Equations

Answer explanation

In the expression 4x + 7, the term 4x represents the variable x multiplied by the coefficient 4. Therefore, 4x is a term in the expression, while 4 and 7 are constants, and 7x is not present.

Answer explanation

In the expression 5y - 3, the coefficient of y is the number that multiplies y. Here, 5 is the number in front of y, making the coefficient 5. Therefore, the correct answer is 5.

Michael is building a rectangular garden. He calculates the area by multiplying the length and width. In this context, which of the following best defines a "factor" in his calculation?

• A number added to a variable

• A number or variable multiplied to form a term

• The answer to an equation

• The variable alone

Answer explanation

A "factor" in an algebraic expression refers to a number or variable that is multiplied to form a term. This distinguishes it from addition or other operations, making the correct choice "A number or variable multiplied to form a term."

Answer explanation

To simplify the expression, combine like terms: 2x + 3x = (2 + 3)x = 5x. Therefore, the correct answer is 5x.

Lily has twice as many apples as a certain number, and then she gets five more apples. Translate the total number of apples Lily has into an algebraic expression.

Answer explanation

The phrase "the sum of twice a number and five" translates to 2x + 5. Here, 'twice a number' is represented as 2x, and 'the sum' indicates addition with 5, making 2x + 5 the correct expression.

Answer explanation

To evaluate the expression 3x + 2 when x = 4, substitute 4 for x: 3(4) + 2 = 12 + 2 = 14. Thus, the correct answer is 14.

Liam is thinking about different math statements. Which of the following is an equation?

Answer explanation

An equation is a mathematical statement that asserts the equality of two expressions. The correct choice, x - 5 = 10, is an equation because it includes an equals sign, indicating a relationship between the two sides.

Answer explanation

The expression 6a - 4b + 9 consists of three terms: 6a, -4b, and 9. Each term is separated by a '+' or '-' sign, making the correct choice the one that includes all three terms.

Answer explanation

To solve for x in the equation 2x + 3 = 11, subtract 3 from both sides to get 2x = 8. Then, divide both sides by 2 to find x = 4. Thus, the correct answer is x = 4.

Answer explanation

The coefficient in the term -8y is the numerical factor that multiplies the variable y. In this case, it is -8, making the correct choice -8.