Solve -0.7(x-1)>10.2

$$-0.7(x-1) > 10.2$$

Solve for x

$$x<-\frac{95}{7}$$

Solution Steps

Divide both sides by -0.7. Since -0.7 is negative, the inequality direction is changed.

$$x-1<\frac{10.2}{-0.7}$$

Expand \frac{10.2}{-0.7} by multiplying both numerator and the denominator by 10.

$$x-1<\frac{102}{-7}$$

Fraction \frac{102}{-7} can be rewritten as -\frac{102}{7} by extracting the negative sign.

$$x-1<-\frac{102}{7}$$

Add 1 to both sides.

$$x<-\frac{102}{7}+1$$

Convert 1 to fraction \frac{7}{7}.

$$x<-\frac{102}{7}+\frac{7}{7}$$

Since -\frac{102}{7} and \frac{7}{7} have the same denominator, add them by adding their numerators.

$$x<\frac{-102+7}{7}$$

Add -102 and 7 to get -95.

$$x<-\frac{95}{7}$$