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 given algebraic expressions step by step.

1. For the expression:
   \( 18 - 30x \)
   Substituting \( x = \frac{1}{3} \):
   \( 18 - 30(1/3) \)
   Now calculating \( 30(1/3) \):
   \( 30 \times \frac{1}{3} = 10 \)
   So we have:
   \( 18 - 10 \)
   \( = 8 \)

   Therefore, the first blank is 10.

2. For the second expression:
   \( 2(9 - 15x) \)
   Substituting \( x = \frac{1}{3} \):
   \( 2(9 - 15(1/3)) \)
   Now calculating \( 15(1/3) \):
   \( 15 \times \frac{1}{3} = 5 \)
   So we have:
   \( 2(9 - 5) \)
   \( = 2(4) \)
   \( = 8 \)

   Therefore, the second blank is 4.

Putting it all together, the filled-in blanks are:

18 - 10
2 (9 - 15(1))
2 (9 - 5)

Notice that both expressions simplify to 8, confirming the consistency.