Solve 7r-4:8r+12=6:11

$$7 r - 4 : 8 r + 12 = 6 : 11$$

Solve for r

$$r = -\frac{252}{143} = -1\frac{109}{143} \approx -1.762237762$$

Steps for Solving Linear Equation

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$7r-\frac{1}{2}r+12=\frac{6}{11}$$

Combine 7r and -\frac{1}{2}r to get \frac{13}{2}r.

$$\frac{13}{2}r+12=\frac{6}{11}$$

Subtract 12 from both sides.

$$\frac{13}{2}r=\frac{6}{11}-12$$

Convert 12 to fraction \frac{132}{11}.

$$\frac{13}{2}r=\frac{6}{11}-\frac{132}{11}$$

Since \frac{6}{11} and \frac{132}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{2}r=\frac{6-132}{11}$$

Subtract 132 from 6 to get -126.

$$\frac{13}{2}r=-\frac{126}{11}$$

Multiply both sides by \frac{2}{13}, the reciprocal of \frac{13}{2}.

$$r=-\frac{126}{11}\times \frac{2}{13}$$

Multiply -\frac{126}{11} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$r=\frac{-126\times 2}{11\times 13}$$

Do the multiplications in the fraction \frac{-126\times 2}{11\times 13}.

$$r=\frac{-252}{143}$$

Fraction \frac{-252}{143} can be rewritten as -\frac{252}{143} by extracting the negative sign.

$$r=-\frac{252}{143}$$