Question

Analyzing Work
Angela was given this expression to simplify. Negative 2 (2 x + 1) minus 3 (x + 3). Consider her steps in simplifying: 1. Negative 2 (2 x) + (negative 2) (1) + negative 3 (x) + (negative 3) (3). 2. Negative 4 x + negative 2 + negative 3 x + negative 9. 3. Negative 7 x minus 11.

Which statements are true about the steps Angela used? Check all that apply.
In step 1, she distributed –2 through the parentheses.
In step 1, she distributed 3 through the parentheses.
In step 2, she added the factor to the value inside the parentheses.
In step 2, she multiplied the factor to the value inside the parentheses.
In step 3, she combined like terms.

Answer 1

True:
- In step 1, she distributed –2 through the parentheses. (She wrote –2(2x) and –2(1).)
- In step 2, she multiplied the factor to the value inside the parentheses. (The terms became –4x, –2, –3x, –9.)
- In step 3, she combined like terms. (–4x + –3x = –7x and –2 + –9 = –11.)

False:
- In step 1, she distributed 3 through the parentheses. (She distributed –3, not 3.)
- In step 2, she added the factor to the value inside the parentheses. (She multiplied the factors; no addition of factor to inside occurred.)