Hat are the possible solutions for the following problem?
|x + 3| < 5
You want numbers within 5 of -3. So,
-8 < x < 2
Can you show me this. I keep getting x<2 and x<-8??
either x+3 <0 or x+3 >= 0
case 1: x+3 < 0 (x < -3)
-(x+3) < 5
-x-3 < 5
-x < 8
x > -8
or, -8 < x
case 2: x+3 >= 0 (x >= -3)
x+3 < 5
x < 2
Looks like you may have forgotten to reverse the direction of the inequality when multiplying by a negative number.
Think of the shape of the graph. It's a V shape, and you want everything below the line y=5.
To find the possible solutions for the inequality |x + 3| < 5, follow these steps:
Step 1: Split the inequality into two separate inequalities:
x + 3 < 5 (equation 1)
and
-(x + 3) < 5 (equation 2)
Step 2: Solve equation 1 for x:
x < 5 - 3
x < 2
Step 3: Solve equation 2 for x:
-x - 3 < 5
-x < 5 + 3
-x < 8
Multiply both sides by -1 (since we want x to be positive):
x > -8
Step 4: Combine the two solutions:
x < 2 and x > -8
Therefore, the possible solutions for the inequality |x + 3| < 5 are x values that are less than 2 and greater than -8.