6) \( r+7.6+1+6.5 r=1.88(5-7.1 r)+7.9(4.4 r+2.1) \)

To solve the equation \( r + 7.6 + 1 + 6.5r = 1.88(5 - 7.1r) + 7.9(4.4r + 2.1) \), first, combine like terms on the left side: \[ r + 6.5r + 8.6 = 7.5r + 8.6 \] Now, simplify the right side. Distributing the constants gives us: \[ 1.88 \cdot 5 - 1.88 \cdot 7.1r + 7.9 \cdot 4.4r + 7.9 \cdot 2.1 \] \[ = 9.4 - 13.308r + 34.76r + 15.69 \] Now combine like terms on the right: \[ = 9.4 + 15.69 + (34.76 - 13.308)r \] \[ = 25.09 + 21.452r \] Setting both sides equal results in: \[ 7.5r + 8.6 = 21.452r + 25.09 \] Now bring all \( r \) terms to one side and constant terms to the other: \[ 7.5r - 21.452r = 25.09 - 8.6 \] \[ -13.952r = 16.49 \] Finally, solve for \( r \): \[ r = \frac{16.49}{-13.952} \approx -1.18 \] Thus, the solution to the equation is approximately \( r \approx -1.18 \).