Question

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

Answer 1

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:
\[
r = -1
\]