Solve the compund inequality and graph the solution.
-4<t+2<4
First I did t+2>-4 and I got t>-2 and I did t+2<4 and i got t<2. Then I graphed it and I dot an open dot on 2 and -2. Is this right?
-1<1/2x<1
I did 1/2x>-1 and i got x>-2 and i did 1/2x<1 and i got x<2. I graphed it and put a open dot on 2 and -2. Is this right?
To solve and graph the compound inequalities, follow these steps:
1. Start by solving each inequality individually:
-4 < t+2 < 4
Solving the first inequality:
t+2 > -4
t > -4 - 2
t > -6
Solving the second inequality:
t+2 < 4
t < 4 - 2
t < 2
2. Combine the individual solutions to form the compound solution:
-6 < t < 2
3. Graph the solution on a number line:
Start by plotting a closed dot at -6 and another closed dot at 2. Since the inequality is strict (>, <), the dots should be shaded/open.
Next, draw a line segment or shade between these two dots to indicate all the values that satisfy the inequality.
So the correct graph for -4 < t+2 < 4 would be an open circle at -6, an open circle at 2, and a shaded line segment between them.
Regarding the second inequality, -1 < (1/2)x < 1:
Solving the first inequality:
(1/2)x > -1
x > -1 / (1/2)
x > -2
Solving the second inequality:
(1/2)x < 1
x < 1 / (1/2)
x < 2
The combined solution is:
-2 < x < 2
To graph this compound inequality, follow the same steps as described before:
Plot a closed dot at -2 and another closed dot at 2. Since the inequality is strict (>, <), both dots should be shaded/open.
Draw a line segment or shade between these two dots to indicate all the values that satisfy the inequality.
So the correct graph for -1 < (1/2)x < 1 would be an open circle at -2, an open circle at 2, and a shaded line segment between them.