Fill in the blanks!

Evaluate the expressions below for x = -1/5.
18 - 30x
18 - 30 (-1/5)
18 - _
24

2 (9-15x)
2(9-15(-_/5))
2(9-(-3))
2(_)
_

Notice that I get the same value again when simplified: 24. Since both of these expressions simplify to the same value for two different values of x, then we know that these two expressions must be _.

1 answer

Let's fill in the blanks step by step.

  1. Evaluate the first expression:

    • For \( x = -\frac{1}{5} \): \[ 18 - 30x = 18 - 30\left(-\frac{1}{5}\right) \] \[ = 18 + 30 \cdot \frac{1}{5} \] \[ = 18 + 6 \] \[ = 24 \]

    Now, fill in the blanks:

    • \( 18 - 30(-1/5) = 18 - 6 \)

    Therefore, we fill in the first blank: \( 18 - _ = 18 - 6 \)

  2. Next, evaluate the second expression:

    • For \( x = -\frac{1}{5} \): \[ 2(9 - 15x) = 2(9 - 15\left(-\frac{1}{5}\right)) \] \[ = 2(9 + 15 \cdot \frac{1}{5}) \] \[ = 2(9 + 3) \] \[ = 2 \cdot 12 \] \[ = 24 \]

    Now to fill the blanks:

    • \( 2(9 - 15(-_/5)) = 2(9 - (-3)) \) Since \( 15(-\frac{1}{5}) = -3 \)

    Therefore, we fill in the second blank: \( 2(9 - _) = 2(9 - (-3)) \)

  3. Now we fill the last blank:

    • The last expression evaluated: \( 2(_)\) As from the previous calculations \(2(12) \)

In summary, we can fill out:

  1. \( 18 - 30(-1/5) = 18 - 6 \)
  2. \( 2(9 - 15(-\frac{1}{5})) = 2(9 - (-3)) \)
  3. \( 2(12) \)

Now for the final sentence: "Since both of these expressions simplify to the same value for two different values of x, then we know that these two expressions must be equivalent."

Similar Questions
  1. Fill in the blanks!You should evaluate with numbers other than 0, because sometimes using x = 0 will give a _ equivalency.
    1. answers icon 1 answer
  2. Fill in the blanks.Define equivalent expressions. | Identify expressions that are equivalent by using _ of operations. Evaluate
    1. answers icon 1 answer
  3. Fill in the blanks!Evaluate the algebraic expressions for x = 1/3. 18 - 30x 18 - 30(1/3) 18 - _ 8 2 (9-15x) 2 (9-15(_/3)) 2
    1. answers icon 1 answer
  4. Fill in the blanks!Evaluate the algebraic expressions for x = 1/3. 18 - 30x 18 - 30(1/3) 18 - _ 8 2 (9-15x) 2 (9-15(_/3)) 2
    1. answers icon 1 answer
more similar questions