Question

Ite the solution set in interva (1)/(3)x<-1 or 6x>0 -3

Answer 1

The solution to the inequalities (1/3)x < -1 or 6x > -3 is found by solving each inequality separately, giving x < -3 and x > -1/2, respectively. Therefore, the solution set in interval notation is (-∞, -3) ∪ (-1/2, ∞).

Step-by-step explanation:

The problem involves finding the solution set where either (1)/(3)x < -1 or 6x > -3. To find the solutions, we solve each inequality separately.

For the first inequality, we multiply both sides by 3 to isolate x:

• 3*(1/3)x < 3*(-1)
• x < -3

For the second inequality, we divide both sides by 6:

• 6x/6 > -3/6
• x > -1/2

The solutions to the inequalities are x < -3 and x > -1/2. Because these are joined by 'or,' the complete solution set is the union of both sets:

• x < -3
• x > -1/2

Therefore, in interval notation, the solution is (-∞, -3) ∪ (-1/2, ∞).