1. Solve |2x + 5|< 9
Solve
Absolute Value 2x+5Absolute Value5 is less than 9
|2x + 5|< 9
What happens if x=4?
What happens if x=-7
now what happen if x is between -7 and 4?
To solve the inequality |2x + 5| < 9, we can break it down into two cases: when the expression inside the absolute value is positive, and when it is negative.
Case 1: When 2x + 5 is positive:
In this case, the inequality |2x + 5| < 9 becomes 2x + 5 < 9. We can solve this equation as follows:
2x + 5 < 9
2x < 9 - 5
2x < 4
x < 2
So, for this case, the solution is x < 2.
Case 2: When 2x + 5 is negative:
In this case, the inequality |2x + 5| < 9 becomes -(2x + 5) < 9. We need to be careful when multiplying by -1 as it changes the direction of the inequality. Let's solve this equation:
-(2x + 5) < 9
-2x - 5 < 9
-2x < 9 + 5
-2x < 14
Dividing both sides by -2, remembering to flip the inequality sign:
x > -7
So, for this case, the solution is x > -7.
Since we have two separate cases, the final solution is the combination of the solutions for each case: x < 2 or x > -7.