Solve 1-2*(m-1)<5m-2*(1-m)

$$1 - 2 \cdot ( m - 1 ) < 5 m - 2 \cdot ( 1 - m )$$

Solve for m

$$m>\frac{5}{9}$$

Solution Steps

Use the distributive property to multiply -2 by m-1.

$$1-2m+2<5m-2\left(1-m\right)$$

Add 1 and 2 to get 3.

$$3-2m<5m-2\left(1-m\right)$$

Use the distributive property to multiply -2 by 1-m.

$$3-2m<5m-2+2m$$

Combine 5m and 2m to get 7m.

$$3-2m<7m-2$$

Subtract 7m from both sides.

$$3-2m-7m<-2$$

Combine -2m and -7m to get -9m.

$$3-9m<-2$$

Subtract 3 from both sides.

$$-9m<-2-3$$

Subtract 3 from -2 to get -5.

$$-9m<-5$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$m>\frac{-5}{-9}$$

Fraction \frac{-5}{-9} can be simplified to \frac{5}{9} by removing the negative sign from both the numerator and the denominator.

$$m>\frac{5}{9}$$