Question

b. evaluate the expression from part (a) when $l = 3$. interpret the result.

c. write an expression equivalent to the one from part (a) by using a tabular model.

d. if logan mows 5 lawns each week, how many lawns does eve mow in 8 weeks?

for problems 4–10, multiply.

1. $3(x - 5)$

1. $-(3x - 7)$

1. $\frac{1}{4}(2 + x)$

Explanation:

Problem 4:

Step 1: Apply distributive property

The distributive property states that \( a(b + c)=ab+ac \). For \( 3(x - 5) \), we distribute 3 to both \( x \) and \( - 5 \).
\( 3\times x-3\times5 \)

Step 2: Simplify the products

Calculate \( 3\times x = 3x \) and \( 3\times5=15 \).
\( 3x - 15 \)

Step 1: Apply distributive property of - 1

The expression \( -(3x - 7) \) can be written as \( - 1\times(3x - 7) \). Using the distributive property \( a(b + c)=ab + ac \) (here \( a=-1 \), \( b = 3x \), \( c=-7 \)), we get \( -1\times3x-1\times(-7) \).

Step 2: Simplify the products

Calculate \( - 1\times3x=-3x \) and \( -1\times(-7) = 7 \).
\( -3x + 7 \)

Step 1: Apply distributive property

For \( \frac{1}{4}(2 + x) \), using the distributive property \( a(b + c)=ab+ac \) (here \( a=\frac{1}{4} \), \( b = 2 \), \( c=x \)), we get \( \frac{1}{4}\times2+\frac{1}{4}\times x \).

Step 2: Simplify the products

Calculate \( \frac{1}{4}\times2=\frac{2}{4}=\frac{1}{2} \) and \( \frac{1}{4}\times x=\frac{x}{4} \).
\( \frac{1}{2}+\frac{x}{4} \) (or we can also write it as \( \frac{x}{4}+\frac{1}{2} \))

Answer:

\( 3x - 15 \)

Problem 5: