Question

Solve the system of inequalities:

37−3x>4x−2
19x−51≥5x+27

Answer 1

Given the system of inequalities:
`37-3x>4x-2`

Add 2 to both sides of the equation, we have;

`39-3x > 4x`

Add 3 to both sides we have;

`39>7x`

Divide both sides by 7 we get;

`x < (39)/(7)`

The solution set for this inequality is:
`(-\infty, (39)/(7))`

Given the system of inequalities:
`19x-51\geq 5x+27`

Add 51 to both sides of the equation, we have;

`19 \geq 5x+78`

Subtract 5x from both sides we have;

`14x \geq 78`

Divide both sides by 14 we get;

`x \geq (78)/(14) = (39)/(7)`

or

`x \geq (39)/(7)`

The solution set for this inequality is:
`[(39)/(7), \infty)`

The combined solution for this system of inequality is;
`(-\infty, (39)/(7)) \cap[(39)/(7), \infty)` = ∅