To determine which of the numbers 1, 2, and 3 satisfy the inequality [tex]\( 2x + 1 \geq 7 \)[/tex], let's test each value step-by-step.
1. For [tex]\( x = 1 \)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] into the inequality: [tex]\( 2(1) + 1 \geq 7 \)[/tex].
- Calculate the left side: [tex]\( 2 \cdot 1 + 1 = 2 + 1 = 3 \)[/tex].
- Check the inequality: [tex]\( 3 \geq 7 \)[/tex], which is false.
2. For [tex]\( x = 2 \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the inequality: [tex]\( 2(2) + 1 \geq 7 \)[/tex].
- Calculate the left side: [tex]\( 2 \cdot 2 + 1 = 4 + 1 = 5 \)[/tex].
- Check the inequality: [tex]\( 5 \geq 7 \)[/tex], which is false.
3. For [tex]\( x = 3 \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the inequality: [tex]\( 2(3) + 1 \geq 7 \)[/tex].
- Calculate the left side: [tex]\( 2 \cdot 3 + 1 = 6 + 1 = 7 \)[/tex].
- Check the inequality: [tex]\( 7 \geq 7 \)[/tex], which is true.
Based on this analysis:
- [tex]\( x = 1 \)[/tex] does not satisfy the inequality [tex]\( 2x + 1 \geq 7 \)[/tex].
- [tex]\( x = 2 \)[/tex] does not satisfy the inequality [tex]\( 2x + 1 \geq 7 \)[/tex].
- [tex]\( x = 3 \)[/tex] does satisfy the inequality [tex]\( 2x + 1 \geq 7 \)[/tex].
Therefore, out of the numbers 1, 2, and 3, only 3 is a solution to the inequality [tex]\( 2x + 1 \geq 7 \)[/tex].
