Complete the process of solving the equation.

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
14(

r–2)–10r=

4

14r–28–10r=

4
Add 14 to both sides
Subtract 14 from both sides
Multiply both sides by 14
Divide both sides by 14
Apply the distributive property
–28=

4
Combine like terms

24r=24
Add 28 to both sides
Subtract 28 from both sides
Multiply both sides by 28
Divide both sides by 28
Apply the distributive property
r=
Divide both sides by

24

1 answer

Let's complete the process step by step:

  1. Start with the original equation: \[ 14(-r - 2) - 10r = -4 \]

  2. Apply the distributive property: \[ 14 \cdot -r + 14 \cdot -2 - 10r = -4 \] This simplifies to: \[ -14r - 28 - 10r = -4 \]

  3. Combine like terms: \[ -14r - 10r - 28 = -4 \] Which simplifies to: \[ -24r - 28 = -4 \]

  4. Now add 28 to both sides: \[ -24r - 28 + 28 = -4 + 28 \] Simplifying gives: \[ -24r = 24 \]

  5. Next, divide both sides by -24: \[ r = \frac{24}{-24} \] Simplifying this results in: \[ r = -1 \]

Now, filling in the missing terms and descriptions:

  • The first part complete: \[ -28 = -4 \quad \text{(after distributing and simplifying)} \]

  • Missing descriptions:

    • Apply the distributive property
    • Combine like terms
    • Add 28 to both sides
    • Divide both sides by -24

Final answer: \[ r = -1 \]