To determine which symbol can be placed in the inequality [tex]\(2x\)[/tex] to create an inequality that will be satisfied by [tex]\(x = 10\)[/tex], [tex]\(x = 11\)[/tex], [tex]\(x = 12\)[/tex], let's analyze each possible symbol:
1. Less than ([tex]\(<\)[/tex]):
- For [tex]\(x = 10\)[/tex]: [tex]\(2 \times 10 = 20 < 10\)[/tex] (this is false)
- So, the symbol [tex]\(<\)[/tex] does not work because the inequality is not satisfied for [tex]\(x = 10\)[/tex].
2. Greater than ([tex]\(>\)[/tex]):
- For [tex]\(x = 10\)[/tex]: [tex]\(2 \times 10 = 20 > 10\)[/tex] (this is true)
- For [tex]\(x = 11\)[/tex]: [tex]\(2 \times 11 = 22 > 11\)[/tex] (this is true)
- For [tex]\(x = 12\)[/tex]: [tex]\(2 \times 12 = 24 > 12\)[/tex] (this is true)
- So, the symbol [tex]\(>\)[/tex] works because the inequality is satisfied for [tex]\(x = 10\)[/tex], [tex]\(x = 11\)[/tex], and [tex]\(x = 12\)[/tex].
3. Less than or equal to ([tex]\(\leq\)[/tex]):
- For [tex]\(x = 10\)[/tex]: [tex]\(2 \times 10 = 20 \leq 10\)[/tex] (this is false)
- So, the symbol [tex]\(\leq\)[/tex] does not work because the inequality is not satisfied for [tex]\(x = 10\)[/tex].
4. Greater than or equal to ([tex]\(\geq\)[/tex]):
- For [tex]\(x = 10\)[/tex]: [tex]\(2 \times 10 = 20 \geq 10\)[/tex] (this is true)
- For [tex]\(x = 11\)[/tex]: [tex]\(2 \times 11 = 22 \geq 11\)[/tex] (this is true)
- For [tex]\(x = 12\)[/tex]: [tex]\(2 \times 12 = 24 \geq 12\)[/tex] (this is true)
- So, the symbol [tex]\(\geq\)[/tex] works because the inequality is satisfied for [tex]\(x = 10\)[/tex], [tex]\(x = 11\)[/tex], and [tex]\(x = 12\)[/tex].
Thus, the correct symbol to place in the inequality [tex]\(2x ? x\)[/tex] that makes [tex]\(x = 10\)[/tex], [tex]\(x = 11\)[/tex], and [tex]\(x = 12\)[/tex] all valid solutions is:
[tex]\[
>
\][/tex]
