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?
no one is answering.
You made a small arithmetic error in
t+2>-4
Should have been t > -6
Actually the easiest way to do these questions is to leave the compound inequality as it it and simply perform operations to isolate the variable between the two inequality signs.
In this case:
-4<t+2<4 , now subtract 2 from each of the 3 parts
-4-2 < t+2-2 < 4-2
-6 < t < 2
Place an open dot on the -6 and the 2 and join with a solid line
is the second queston right?
To solve the compound inequality -4 < t + 2 < 4, you correctly set up two separate inequalities:
1. t + 2 > -4
2. t + 2 < 4
Now we can solve these inequalities individually:
From the first inequality, t + 2 > -4, subtracting 2 from both sides gives: t > -6.
From the second inequality, t + 2 < 4, subtracting 2 from both sides gives: t < 2.
So, the solution to the compound inequality is -6 < t < 2.
To graph this solution, you can draw a number line with -6 on the left and 2 on the right. Since the inequality symbols in the original problem are not inclusive but strict (i.e., < and >), you need to use open dots on the endpoints -6 and 2. Finally, shade the region between -6 and 2.
Regarding the second compound inequality, -1 < (1/2)x < 1, you set up the inequalities correctly:
1. (1/2)x > -1
2. (1/2)x < 1
Now, let's solve them:
From the first inequality, (1/2)x > -1, multiplying both sides by 2 gives: x > -2.
From the second inequality, (1/2)x < 1, multiplying both sides by 2 gives: x < 2.
So, the solution to the compound inequality is -2 < x < 2.
You can graph this solution by drawing a number line with -2 on the left and 2 on the right. Since the inequality symbols in the original problem are not inclusive but strict (i.e., < and >), you need to use open dots on the endpoints -2 and 2. Finally, shade the region between -2 and 2.
Hence, your graph is correct. Well done!