To solve the equation [tex]\(\frac{3(5 + 2r)}{6} - 5 = 4\)[/tex], follow these steps:
### Step 1: Eliminate the fraction
Multiply both sides of the equation by 6 to remove the denominator:
[tex]\[
6 \cdot \left(\frac{3(5 + 2r)}{6} - 5\right) = 6 \cdot 4
\][/tex]
This simplifies to:
[tex]\[
3(5 + 2r) - 30 = 24
\][/tex]
### Step 2: Distribute through the parentheses
Next, distribute the 3 across the terms inside the parentheses:
[tex]\[
3 \cdot 5 + 3 \cdot 2r - 30 = 24
\][/tex]
This simplifies to:
[tex]\[
15 + 6r - 30 = 24
\][/tex]
### Step 3: Combine like terms
Combine the constant terms on the left side:
[tex]\[
6r - 15 = 24
\][/tex]
### Step 4: Isolate the variable term
Add 15 to both sides to isolate the term with [tex]\(r\)[/tex]:
[tex]\[
6r - 15 + 15 = 24 + 15
\][/tex]
This simplifies to:
[tex]\[
6r = 39
\][/tex]
### Step 5: Solve for [tex]\(r\)[/tex]
Finally, divide both sides by 6 to solve for [tex]\(r\)[/tex]:
[tex]\[
r = \frac{39}{6}
\][/tex]
Simplify the fraction:
[tex]\[
r = 6.5
\][/tex]
Hence, the solution to the equation [tex]\(\frac{3(5 + 2r)}{6} - 5 = 4\)[/tex] is [tex]\(r = 6.5\)[/tex].
