https://file.aiquickdraw.com/mathbot/file/1725991559703njn8vs44.jpg

The equation shown in the image is:

\[
\frac{7}{8}r = \frac{1}{4}(3r - 2) - 7 + \frac{3}{4}r
\]

Let's solve this step-by-step for \( r \).

### Step 1: Distribute on the right-hand side
Distribute \( \frac{1}{4} \) over the expression \( (3r - 2) \):

\[
\frac{1}{4}(3r - 2) = \frac{1}{4} \times 3r - \frac{1}{4} \times 2 = \frac{3}{4}r - \frac{2}{4} = \frac{3}{4}r - \frac{1}{2}
\]

So, the equation becomes:

\[
\frac{7}{8}r = \frac{3}{4}r - \frac{1}{2} - 7 + \frac{3}{4}r
\]

### Step 2: Combine like terms on the right-hand side
Combine \( \frac{3}{4}r \) and \( \frac{3}{4}r \) on the right-hand side:

\[
\frac{7}{8}r = \left( \frac{3}{4}r + \frac{3}{4}r \right) - \frac{1}{2} - 7 = \frac{6}{4}r - \frac{1}{2} - 7
\]

Simplify \( \frac{6}{4}r \) to \( \frac{3}{2}r \):

\[
\frac{7}{8}r = \frac{3}{2}r - \frac{1}{2} - 7
\]

### Step 3: Simplify further
Now, combine constants on the right-hand side:

\[
\frac{7}{8}r = \frac{3}{2}r - \left(\frac{1}{2} + 7\right) = \frac{3}{2}r - \frac{15}{2}
\]

### Step 4: Eliminate fractions
To eliminate fractions, multiply the entire equation by 8 (the least common denominator of 8 and 2):

\[
8 \times \frac{7}{8}r = 8 \times \left( \frac{3}{2}r - \frac{15}{2} \right)
\]

This simplifies to:

\[
7r = 12r - 60
\]

### Step 5: Solve for \( r \)
Now, subtract \( 12r \) from both sides:

\[
7r - 12r = -60
\]

\[
-5r = -60
\]

Finally, divide by \( -5 \):

\[
r = \frac{-60}{-5} = 12
\]

Thus, the solution is:

\[
r = 12
\]

Would you like any further details or clarifications?

### Related Questions:
1. How can you eliminate fractions more efficiently in equations like this?
2. Why is distributing terms important in algebraic simplifications?
3. What is the general strategy for solving equations involving variables on both sides?
4. How can you verify your solution to ensure it's correct?
5. What happens if you accidentally forget to combine like terms?

### Tip:
When solving equations with fractions, multiplying through by the least common denominator (LCD) early can simplify calculations.

Solve for r: (7/8)r = (1/4)(3r - 2) - 7 + (3/4)r

Learn how to solve the linear equation (7/8)r = (1/4)(3r - 2) - 7 + (3/4)r. This problem covers key algebraic concepts such as solving equations with fractions, using the distributive property, and combining like terms. Suitable for students in Grades 8-10.

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