### For the first inequality: [tex]\(2x - 3 < -9\)[/tex]
Let's solve this step-by-step:
1. Starting Inequality:
[tex]\[
2x - 3 < -9
\][/tex]
2. Add 3 to both sides:
[tex]\[
2x - 3 + 3 < -9 + 3
\][/tex]
[tex]\[
2x < -6
\][/tex]
3. Divide both sides by 2:
[tex]\[
\frac{2x}{2} < \frac{-6}{2}
\][/tex]
[tex]\[
x < -3
\][/tex]
Now, we need to test each of the given values to see if they satisfy [tex]\(x < -3\)[/tex]:
- [tex]\(x = -10:\)[/tex] [tex]\(-10 < -3\)[/tex] (True)
- [tex]\(x = -4:\)[/tex] [tex]\(-4 < -3\)[/tex] (True)
- [tex]\(x = -3:\)[/tex] [tex]\(-3 < -3\)[/tex] (False)
- [tex]\(x = -2:\)[/tex] [tex]\(-2 < -3\)[/tex] (False)
- [tex]\(x = 3:\)[/tex] [tex]\(3 < -3\)[/tex] (False)
So, the values that satisfy [tex]\(2x - 3 < -9\)[/tex] are:
- [tex]\(x = -10\)[/tex]
- [tex]\(x = -4\)[/tex]
### For the second inequality: [tex]\(-3x + 2 < 5\)[/tex]
Let's solve this step-by-step:
1. Starting Inequality:
[tex]\[
-3x + 2 < 5
\][/tex]
2. Subtract 2 from both sides:
[tex]\[
-3x + 2 - 2 < 5 - 2
\][/tex]
[tex]\[
-3x < 3
\][/tex]
3. Divide both sides by -3 and reverse the inequality (since dividing by a negative number reverses the direction):
[tex]\[
\frac{-3x}{-3} > \frac{3}{-3}
\][/tex]
[tex]\[
x > -1
\][/tex]
Now, we need to test each of the given values to see if they satisfy [tex]\(x > -1\)[/tex]:
- [tex]\(x = -3:\)[/tex] [tex]\(-3 > -1\)[/tex] (False)
- [tex]\(x = -2:\)[/tex] [tex]\(-2 > -1\)[/tex] (False)
- [tex]\(x = -1:\)[/tex] [tex]\(-1 > -1\)[/tex] (False)
- [tex]\(x = 0:\)[/tex] [tex]\(0 > -1\)[/tex] (True)
- [tex]\(x = 1:\)[/tex] [tex]\(1 > -1\)[/tex] (True)
So, the values that satisfy [tex]\(-3x + 2 < 5\)[/tex] are:
- [tex]\(x = 0\)[/tex]
- [tex]\(x = 1\)[/tex]
### Summary
1. Circle the values that are solutions of the inequality [tex]\(2x - 3 < -9\)[/tex]. Circle all that apply.
- [tex]\(x = -10\)[/tex]
- [tex]\(x = -4\)[/tex]
2. Circle the values that are solutions of the inequality [tex]\(-3x + 2 < 5\)[/tex]. Circle all that apply.
- [tex]\(x = 0\)[/tex]
- [tex]\(x = 1\)[/tex]
