Fill in the blanks!

Question

Evaluate the algebraic expressions for x = 1/3.
18 - 30x
18 - 30(1/3)
18 - _
8

2 (9-15x)
2 (9-15(_/3))
2 (9-5)
2 (_)
8
Notice that I end up with the same value for each, when simplified.

Answer 1

Let's evaluate the algebraic expressions step by step for \( x = \frac{1}{3} \).

1. Expression: \( 18 - 30x \)

   Substituting \( x = \frac{1}{3} \): \[ 18 - 30 \left(\frac{1}{3}\right) = 18 - 30 \cdot \frac{1}{3} = 18 - 10 = 8 \]

   Filling in the blank: \[ 18 - 30\left(\frac{1}{3}\right) = 18 - 10 \quad \Rightarrow \quad 10 \]

2. Expression: \( 2(9 - 15x) \)

   Substituting \( x = \frac{1}{3} \): \[ 2\left(9 - 15\left(\frac{1}{3}\right)\right) = 2\left(9 - 15 \cdot \frac{1}{3}\right) = 2\left(9 - 5\right) = 2 \cdot 4 = 8 \]

   Filling in the blank: \[ 2(9 - 15x) = 2(9 - 15\left(\frac{1}{3}\right)) = 2(9 - 5) \quad \Rightarrow \quad 4 \]

Thus, the filled blanks are:

1. \( 10 \)
2. \( 4 \)

Both calculations lead to the final value of \( 8 \) when simplified.