Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
14r+14–7r=5r+8
7r+14=5r+8
Add 14r to both sides
Subtract 14r from both sides
Multiply both sides by 14r
Divide both sides by 14r
Combine like terms
+14=8 Subtract 5r from both sides
2r=
–
6
Add 14 to both sides
Subtract 14 from both sides
Multiply both sides by 14
Divide both sides by 14
Apply the distributive property
r=
Divide both sides by 2

Answer 1

Let's complete the process of solving the equation step by step. The original equation is:

\[ 14r + 14 - 7r = 5r + 8 \]

Step 1: Combine like terms on the left side of the equation.

Combine \(14r\) and \(-7r\):

\[ (14r - 7r) + 14 = 5r + 8 \]

This simplifies to:

\[ 7r + 14 = 5r + 8 \]

Step 2: Subtract \(5r\) from both sides.

Next, subtract \(5r\) from both sides to isolate the terms related to \(r\):

\[ 7r - 5r + 14 = 8 \]

This simplifies to:

\[ 2r + 14 = 8 \]

Step 3: Subtract 14 from both sides.

Now, subtract \(14\) from both sides:

\[ 2r + 14 - 14 = 8 - 14 \]

This simplifies to:

\[ 2r = -6 \]

Step 4: Divide both sides by 2.

Next, divide both sides by \(2\) to solve for \(r\):

\[ r = \frac{-6}{2} \]

This simplifies to:

\[ r = -3 \]

Summary:

Thus, the solutions can be summarized as follows:

1. Original equation: \(14r + 14 - 7r = 5r + 8\)
2. Combine like terms: \(7r + 14 = 5r + 8\)
3. Subtract \(5r\) from both sides: \(2r + 14 = 8\)
4. Subtract \(14\) from both sides: \(2r = -6\)
5. Divide both sides by \(2\): \(r = -3\)

Final Answer:

\(r = -3\)