Question

part b – algebraic expressions (variables & constants)

1. write an algebraic expression for:

“four more than twice a number x.”

1. identify the terms, coefficients, and constants in this expression:

7y - 3 + 4y

Explanation:

Question 3

Step1: Analyze "twice a number x"

"Twice a number x" means multiplying \( x \) by 2, so that's \( 2x \).

Step2: Analyze "four more than"

"Four more than" means adding 4 to the previous result. So we add 4 to \( 2x \).

First, simplify the expression \( 7y - 3 + 4y \) by combining like terms. Like terms are terms with the same variable (or constant terms).

• Combine the \( y \)-terms: \( 7y + 4y = 11y \), so the simplified expression is \( 11y - 3 \).

Now, identify terms, coefficients, and constants:

• Terms: In an algebraic expression, terms are separated by addition or subtraction. In the simplified expression \( 11y - 3 \), the terms are \( 11y \) and \( -3 \) (or in the original expression \( 7y \), \( -3 \), and \( 4y \)).
• Coefficients: A coefficient is the numerical factor of a term with a variable. For the term \( 11y \) (or \( 7y \) and \( 4y \) in the original), the coefficient of \( 7y \) is 7, the coefficient of \( 4y \) is 4, and in the simplified term \( 11y \), the coefficient is 11.
• Constants: A constant is a term without a variable. In both the original and simplified expressions, the constant term is \( -3 \) (or 3 with a negative sign; the constant is the number that doesn't change with the variable, so it's -3 here).

Answer:

\( 2x + 4 \)

Question 4