Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Let's analyze each inequality and determine which one will have an open circle when graphed on a number line.
1. [tex]\( x > \frac{3}{5} \)[/tex]:
- "Greater than" ([tex]\(>\)[/tex]) is a strict inequality, meaning that [tex]\( x \)[/tex] can be any value greater than [tex]\( \frac{3}{5} \)[/tex], but not equal to [tex]\( \frac{3}{5} \)[/tex].
- When graphed, a strict inequality is represented with an open circle at [tex]\( \frac{3}{5} \)[/tex], indicating that [tex]\( \frac{3}{5} \)[/tex] is not included in the solution set.
2. [tex]\( \frac{4}{7} \geq x \)[/tex]:
- "Greater than or equal to" ([tex]\(\geq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or less than [tex]\( \frac{4}{7} \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( \frac{4}{7} \)[/tex], indicating that [tex]\( \frac{4}{7} \)[/tex] is included in the solution set.
3. [tex]\( x \leq 12 \)[/tex]:
- "Less than or equal to" ([tex]\(\leq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or less than [tex]\( 12 \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( 12 \)[/tex], indicating that [tex]\( 12 \)[/tex] is included in the solution set.
4. [tex]\( x \geq -6 \)[/tex]:
- "Greater than or equal to" ([tex]\(\geq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or greater than [tex]\( -6 \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( -6 \)[/tex], indicating that [tex]\( -6 \)[/tex] is included in the solution set.
The inequality [tex]\( x > \frac{3}{5} \)[/tex] involves a strict inequality and, therefore, will have an open circle when graphed on a number line.
Thus, the answer is:
[tex]\[ x > \frac{3}{5} \][/tex]
1. [tex]\( x > \frac{3}{5} \)[/tex]:
- "Greater than" ([tex]\(>\)[/tex]) is a strict inequality, meaning that [tex]\( x \)[/tex] can be any value greater than [tex]\( \frac{3}{5} \)[/tex], but not equal to [tex]\( \frac{3}{5} \)[/tex].
- When graphed, a strict inequality is represented with an open circle at [tex]\( \frac{3}{5} \)[/tex], indicating that [tex]\( \frac{3}{5} \)[/tex] is not included in the solution set.
2. [tex]\( \frac{4}{7} \geq x \)[/tex]:
- "Greater than or equal to" ([tex]\(\geq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or less than [tex]\( \frac{4}{7} \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( \frac{4}{7} \)[/tex], indicating that [tex]\( \frac{4}{7} \)[/tex] is included in the solution set.
3. [tex]\( x \leq 12 \)[/tex]:
- "Less than or equal to" ([tex]\(\leq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or less than [tex]\( 12 \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( 12 \)[/tex], indicating that [tex]\( 12 \)[/tex] is included in the solution set.
4. [tex]\( x \geq -6 \)[/tex]:
- "Greater than or equal to" ([tex]\(\geq\)[/tex]) is a non-strict inequality, meaning that [tex]\( x \)[/tex] can be equal to or greater than [tex]\( -6 \)[/tex].
- When graphed, a non-strict inequality is represented with a closed circle at [tex]\( -6 \)[/tex], indicating that [tex]\( -6 \)[/tex] is included in the solution set.
The inequality [tex]\( x > \frac{3}{5} \)[/tex] involves a strict inequality and, therefore, will have an open circle when graphed on a number line.
Thus, the answer is:
[tex]\[ x > \frac{3}{5} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.