Please help me graph this
Absolute value x+1 inside absolute brackets -3<4
Where would this be on a graph line?
Not clear just what you mean, but if it's
|x+1| - 3 < 3
|x+1| < 6
Then either x+1 >= 0 (x >= 1) and
x+1 < 6
x < 5
or x+1 < 0 (x < -1) and
-(x+1) < 6
-x < 7
x > -7
So, we have
-7 < x < -1 or -1<=x<5
that is,
-7 < x < 5
original problem was <4 at the end not <3....thanks for your help...It was hard to explain.
Oops. My bad. Make the change and solve again. The key is to solve for the two cases where the expression in || is positive or negative.
To graph the inequality |x + 1| < 4, we can follow these steps:
Step 1: Break the inequality into two separate inequalities without absolute value:
x + 1 < 4 and -(x + 1) < 4
Step 2: Solve each inequality separately:
For the first inequality, x + 1 < 4, subtract 1 from both sides:
x < 3
For the second inequality, -(x + 1) < 4, multiply both sides by -1, which reverses the inequality:
x + 1 > -4
x > -5
Step 3: Combine the two inequalities:
-5 < x < 3
In graph form, you would plot a solid dot at x = -5 and another solid dot at x = 3. Then, draw a solid line connecting these two dots to represent all the values between -5 and 3. The shaded region on the number line between the dots represents where the inequality |x + 1| < 4 is true. Any value within this range satisfies the inequality.
Here is a visual representation of the graph on a number line:
--------●-----------------●--------
-6 -5 -4 -3 -2 -1 0 1 2 3 4