Solve 19r-105/-1=21-72r/-2

$$\frac { 19 r - 105 } { - 1 } = \frac { 21 - 72 r } { - 2 }$$

Solve for r

$$r = \frac{21}{10} = 2\frac{1}{10} = 2.1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2, the least common multiple of -1,-2.

$$-2\left(19r-105\right)=-\left(21-72r\right)$$

Use the distributive property to multiply -2 by 19r-105.

$$-38r+210=-\left(21-72r\right)$$

To find the opposite of 21-72r, find the opposite of each term.

$$-38r+210=-21-\left(-72r\right)$$

The opposite of -72r is 72r.

$$-38r+210=-21+72r$$

Subtract 72r from both sides.

$$-38r+210-72r=-21$$

Combine -38r and -72r to get -110r.

$$-110r+210=-21$$

Subtract 210 from both sides.

$$-110r=-21-210$$

Subtract 210 from -21 to get -231.

$$-110r=-231$$

Divide both sides by -110.

$$r=\frac{-231}{-110}$$

Reduce the fraction \frac{-231}{-110} to lowest terms by extracting and canceling out -11.

$$r=\frac{21}{10}$$