Question

How do you solve `\frac{1}{4} x + \frac{7}{2} < \frac{3}{4} - \frac{5}{2} x`?

Answer 1

See explanation.

Explanation:

The starting inequality is:

`1/4x+7/2<3/4-5/2x`

The ferst step to solve it to multiply by the least common multiplier (4) to transform all numbers to integers.

`x+14<3-10x`

Now we have to move terms with `x` to one side and numbers to other.

`x+10x<3-14`

`11x<-11`

Final step is to divide both sides by `11`.

`x<-1`

Finally the answer is `x<-1` or in interval form `x in (-oo;-1)`