To find the smallest integer that satisfies the inequality [tex]\(3x \geq 16\)[/tex], follow these steps:
1. Start with the given inequality:
[tex]\[ 3x \geq 16 \][/tex]
2. Isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by 3:
[tex]\[ x \geq \frac{16}{3} \][/tex]
3. Calculate the value of [tex]\(\frac{16}{3}\)[/tex]:
[tex]\[ \frac{16}{3} = 5.333333333333333 \][/tex]
4. Identify the smallest integer greater than or equal to [tex]\(5.333333333333333\)[/tex] (since [tex]\(x\)[/tex] must be an integer):
[tex]\[ \lceil 5.333333333333333 \rceil = 6 \][/tex]
Therefore, the smallest integer that satisfies the inequality [tex]\(3x \geq 16\)[/tex] is:
[tex]\[ x = 6 \][/tex]
