|2x+9|<25

how do you solve this?

when yyour done can you give me examples to try on my own?

To solve the inequality |2x + 9| < 25, we can follow these steps:

Step 1: Split the inequality into two separate inequalities without the absolute value symbol.

|2x + 9| < 25
This can be written as:
2x + 9 < 25 and -(2x + 9) < 25

Step 2: Solve each inequality separately. Start with the first one:

2x + 9 < 25
Subtract 9 from both sides:
2x < 25 - 9
2x < 16
Divide both sides by 2 (since the coefficient is positive):
x < 8

Step 3: Solve the second inequality:

-(2x + 9) < 25
Multiply both sides by -1 to change the direction of the inequality:
2x + 9 > -25
Subtract 9 from both sides:
2x > -25 - 9
2x > -34
Divide both sides by 2 (since the coefficient is positive):
x > -17

Step 4: Combine the two solutions:

x < 8 and x > -17

To find examples to try on your own, you can substitute different values for x in the original inequality and see if they satisfy the inequality. For example, let's substitute x = 5:

|2(5) + 9| < 25
|10 + 9| < 25
|19| < 25
As 19 is less than 25, this value satisfies the inequality. You can try substituting other values and see if they satisfy the inequality as well.