Solve for r
r = -\frac{11}{2} = -5\frac{1}{2} = -5.5
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\left(r-2\right)\times 5=\left(r-7\right)\times 3
Variable r cannot be equal to any of the values 2,7 since division by zero is not defined. Multiply both sides of the equation by \left(r-7\right)\left(r-2\right), the least common multiple of r-7,r-2.
5r-10=\left(r-7\right)\times 3
Use the distributive property to multiply r-2 by 5.
5r-10=3r-21
Use the distributive property to multiply r-7 by 3.
5r-10-3r=-21
Subtract 3r from both sides.
2r-10=-21
Combine 5r and -3r to get 2r.
2r=-21+10
Add 10 to both sides.
2r=-11
Add -21 and 10 to get -11.
r=\frac{-11}{2}
Divide both sides by 2.
r=-\frac{11}{2}
Fraction \frac{-11}{2} can be rewritten as -\frac{11}{2} by extracting the negative sign.
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