Question

Solve the inequality graph the solution set and write it in interval notation x-6<5(x+2)

Answer 1

x>-4

Explanation:

x-6>5x+10

x-5x>10+6

-4x<16

x<16/-4

x<-4

Answer 2

The solution set in interval notation: (-∞, -4)

How to determine solution of an inequality

Let's solve the inequality x - 6 < 5(x + 2)

Distribute the 5 on the right side:

x - 6 < 5x + 10

Subtract x from both sides:

-6 < 4x + 10

Subtract 10 from both sides:

-16 < 4x

Divide both sides by 4 (remember to reverse the inequality sign when dividing by a negative number):

-4 < x

Now, let's graph the solution set on a number line: The broken line indicate that the boundary line value is not included in the solution. The feasible region included values less than -4 and extend to negative infinity.

The open circle at -4 indicates that -4 is not included in the solution.

Finally, express the solution set in interval notation: (-∞, -4)