Sure, let's go through the steps to prove whether [tex]\( x = -3 \)[/tex] satisfies the inequality [tex]\( -4x < 8 \)[/tex].
### Step-by-Step Solution:
1. Substitute [tex]\( x = -3 \)[/tex] into the inequality:
- The given inequality is [tex]\( -4x < 8 \)[/tex].
- Substitute [tex]\( x = -3 \)[/tex] into the left-hand side of the inequality:
[tex]\[
-4(-3)
\][/tex]
2. Simplify the left-hand side:
- When we multiply [tex]\(-4\)[/tex] by [tex]\(-3\)[/tex], we get:
[tex]\[
-4 \times (-3) = 12
\][/tex]
3. Evaluate the inequality:
- Substitute [tex]\( 12 \)[/tex] back in for the left-hand side:
[tex]\[
12 < 8
\][/tex]
- Now, let's evaluate whether this statement is true or false.
4. Check the truth of the statement:
- Clearly, [tex]\( 12 \)[/tex] is not less than [tex]\( 8 \)[/tex].
[tex]\[
12 \geq 8
\][/tex]
- Therefore, [tex]\( 12 < 8 \)[/tex] is a false statement.
### Conclusion:
Since the statement [tex]\( 12 < 8 \)[/tex] is false, it means that substituting [tex]\( x = -3 \)[/tex] into the inequality [tex]\( -4x < 8 \)[/tex] does not satisfy the inequality. Thus, [tex]\( x = -3 \)[/tex] is not in the solution set of the inequality [tex]\( -4x < 8 \)[/tex].
