To determine whether the number 4 is a solution to the inequality [tex]\(\frac{1}{2} x - 3 \leq -3\)[/tex], we need to follow these steps:
1. Substitute the number [tex]\(x = 4\)[/tex] into the inequality.
2. Evaluate the left-hand side of the inequality after the substitution.
3. Compare the result to the right-hand side of the inequality to see if it holds true.
Let's substitute [tex]\(x = 4\)[/tex] into the inequality:
[tex]\[
\frac{1}{2} \cdot 4 - 3 \leq -3
\][/tex]
First, compute [tex]\(\frac{1}{2} \cdot 4\)[/tex]:
[tex]\[
\frac{1}{2} \cdot 4 = 2
\][/tex]
Next, subtract 3 from the result:
[tex]\[
2 - 3 = -1
\][/tex]
Now, compare [tex]\(-1\)[/tex] to [tex]\(-3\)[/tex] to check if the inequality holds:
[tex]\[
-1 \leq -3
\][/tex]
Since [tex]\(-1\)[/tex] is not less than or equal to [tex]\(-3\)[/tex], the inequality does not hold true. Therefore, the number 4 is not a solution to the inequality [tex]\(\frac{1}{2} x - 3 \leq -3\)[/tex].
The answer is:
False
