Question

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Explanation:

Step1: Simplify the right side

After subtracting $\frac{3}{4}r$ from both sides, the right side is $r - \frac{3}{4}r + 15$. Since $r = \frac{4}{4}r$, we have $\frac{4}{4}r - \frac{3}{4}r=\frac{1}{4}r$. So the right side becomes $\frac{1}{4}r + 15$.

Step2: Solve for r

Now we have the equation $9=\frac{1}{4}r + 15$. Subtract 15 from both sides: $9 - 15=\frac{1}{4}r$. So $- 6=\frac{1}{4}r$. Multiply both sides by 4: $r=-6\times4=-24$. But first, let's complete the step from the given work. After the subtraction of $\frac{3}{4}r$ from both sides, the right side simplifies to $\frac{1}{4}r + 15$. So the box on the right after the subtraction step (before solving for r) should be $\frac{1}{4}r + 15$. But if we continue to solve for r:

Step3: Isolate r term

From $9=\frac{1}{4}r + 15$, subtract 15: $9 - 15=\frac{1}{4}r\Rightarrow - 6=\frac{1}{4}r$.

Step4: Solve for r

Multiply both sides by 4: $r=-6\times4 = - 24$.

But based on the given work (the subtraction step), the right side after subtracting $\frac{3}{4}r$ is $\frac{1}{4}r + 15$. If we are to fill the box in the given step (after subtraction), the expression is $\frac{1}{4}r + 15$. But if the question is to find r, then:

(for finding r):

Step1: Subtract $\frac{3}{4}r$ from both sides

We get $9 = r-\frac{3}{4}r + 15$.

Step2: Simplify r terms

$r-\frac{3}{4}r=\frac{1}{4}r$, so $9=\frac{1}{4}r + 15$.

Step3: Subtract 15 from both sides

$9 - 15=\frac{1}{4}r\Rightarrow - 6=\frac{1}{4}r$.

Step4: Multiply by 4

$r=-6\times4=-24$.

Answer:

If filling the box after subtraction: $\frac{1}{4}r + 15$; if finding r: $r = - 24$