Answer:
The answer is [tex]r = - \frac{1}{5}[/tex] .
Step-by-step explanation:
-Solve the equation:
[tex]r + 1 \frac{1}{6} = \frac{29}{30}[/tex]
-Multiply both sides by 30:
[tex]r + 1 \frac{1}{6} = \frac{29}{30}[/tex]
[tex]30r + 5 (1 \times 6 + 1) = 29[/tex]
-Multiply 1 and 6:
[tex]30r + 5 (1 \times 6 + 1) = 29[/tex]
[tex]30r + 5 (6 + 1) = 29[/tex]
-Add 6 and 1:
[tex]30r + 5 (6 + 1) = 29[/tex]
[tex]30r + 5 \times 7 = 29[/tex]
-Multiply 5 and 7:
[tex]30r + 5 \times 7= 29[/tex]
[tex]30r + 35 = 29[/tex]
-Subtract 35 from both sides:
[tex]30r + 35 -35 = 29 -35[/tex]
[tex]30r = -6[/tex]
Divide both sides by 30:
[tex]\frac{30r}{30} = \frac{-6}{30}[/tex]
[tex]r = \frac{-6}{30}[/tex]
-Simplify:
[tex]r = \frac{-6}{30}[/tex]
[tex]r = - \frac{1}{5}[/tex]
So, the final answer is [tex]r = -\frac{1}{5}[/tex]
