I need help with this question please:
Solve the inequality. Give the result in set notation. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
-25 5x < 30
{x | 1 x < 2}
To solve the inequality -25 + 5x < 30, follow these steps:
1. Start by subtracting -25 from both sides of the equation:
-25 + 5x - (-25) < 30 - (-25)
5x < 30 + 25
5x < 55
2. Next, divide both sides of the equation by 5:
(5x)/5 < 55/5
x < 11
So, the solution to the inequality is x < 11.
Now let's express this solution in set notation. Since x can be any number less than 11 but not equal to 11, we can write the solution as:
{x | x < 11, x ≠ 11}
Here, the vertical bar "|" separates the variable x from the conditions of the inequality, and the comma "," represents "and." The condition x ≠ 11 means that x cannot be equal to 11.