Complete the process of solving the equation.

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

5(

14r–12)=

10
70r+60=

10
Add -5 to both sides
Subtract -5 from both sides
Multiply both sides by -5
Divide both sides by -5
Apply the distributive property
70r=
Subtract 60 from both sides
r=
Divide both sides by 70

1 answer

Let's complete the process of solving the equation step by step.

  1. Start with the equation:

\[ -5(-14r - 12) = -10 \]

  1. Apply the distributive property:

\[ -5 \cdot -14r - 5 \cdot -12 = -10 \]

This simplifies to:

\[ 70r + 60 = -10 \]

  1. Now we have the equation:

\[ 70r + 60 = -10 \]

  1. Next, we will subtract 60 from both sides:

\[ 70r + 60 - 60 = -10 - 60 \]

This simplifies to:

\[ 70r = -70 \]

  1. Now we need to divide both sides by 70:

\[ \frac{70r}{70} = \frac{-70}{70} \]

This simplifies to:

\[ r = -1 \]

So we have filled in the missing terms, described the steps, and simplified any fractions for the equation solving process.

Here’s the process summarized with missing terms and operations:

  1. Equation: \( -5(-14r - 12) = -10 \)
  2. Apply the distributive property: \( 70r + 60 = -10 \)
  3. Subtract 60 from both sides: \( 70r = -70 \)
  4. Divide both sides by 70: \( r = -1 \)

The missing descriptions:

  • Multiply both sides by -5 (this step was used to initially manipulate the equation).
  • Apply the distributive property.
  • Subtract 60 from both sides.
  • Divide both sides by 70.