5x + 9 – 4x = 17

[?]x – 8 = 8
x = [?]

1 answer

Let's solve the equations step by step.

  1. For the first equation:

    \[ 5x + 9 - 4x = 17 \]

    Combine like terms:

    \[ (5x - 4x) + 9 = 17 \]

    This simplifies to:

    \[ x + 9 = 17 \]

    Now, subtract 9 from both sides:

    \[ x = 17 - 9 \]

    Thus, we find:

    \[ x = 8 \]

  2. For the second equation:

    \[ [?]x - 8 = 8 \]

    We know from the first equation that \( x = 8 \). To fill in the blank, we substitute \( x = 8 \):

    Rewriting the equation:

    \[ k \cdot 8 - 8 = 8 \]

    Now, add 8 to both sides:

    \[ k \cdot 8 = 16 \]

    Divide both sides by 8:

    \[ k = 2 \]

So, the answers are:

  • From the first equation, \( x = 8 \).
  • From the second equation, the missing coefficient is \( 2 \).

Thus, the filled answers are:

  1. \( x = 8 \)
  2. The coefficient is \( 2 \).