# How do solve #x-10/(x-1)>=4# algebraically?

##### 1 Answer

#### Explanation:

Combine the left hand side into one fraction:

Now, there are two possible ways to solve it. The first way is to multiply both sides by

The simpler method would be to directly draw the sign diagram. We first find the zeros of the numerator and denominator. For the numerator, the zeroes are

For the denominator, when

From this, we can determine four ranges where for its sign:

- between
#-oo# and#-1# (the numerator is positive, the denominator is negative; the fraction is negative) - between
#-1# and#1# (the numerator is negative; the denominator is negative; the fraction is positive) - between
#1# and#6# (numerator is negative; the denominator is positive; the fraction is negative) - between
#6# and#oo# (numerator is positive; the denominator is positive; the fraction is positive)

We find that the fraction is greater than

The final solution is thus