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Questions and Answers
What does the inequality X represent?
What does the inequality X represent?
x ≤ 24
When graphing b < 6, would you use an open or closed circle?
When graphing b < 6, would you use an open or closed circle?
- Closed
- Open (correct)
What does the inequality 9 ≥ -2m + 2 − 3 simplify to?
What does the inequality 9 ≥ -2m + 2 − 3 simplify to?
m ≥ -5
What is the solution of the inequality 3(x - 2) < 2(x + 9)?
What is the solution of the inequality 3(x - 2) < 2(x + 9)?
What does the inequality represent: There are no more than 18 students on the hall?
What does the inequality represent: There are no more than 18 students on the hall?
When graphing m ≤ 5, would you use an open or closed circle?
When graphing m ≤ 5, would you use an open or closed circle?
What is the solution for the inequality 12 ≥ 15 - 6y?
What is the solution for the inequality 12 ≥ 15 - 6y?
What inequality could be used to determine how much can be paid monthly for a laptop costing at most $1200?
What inequality could be used to determine how much can be paid monthly for a laptop costing at most $1200?
When graphing x > -14, would you use an open or closed circle?
When graphing x > -14, would you use an open or closed circle?
What does the inequality -p - 4p > -10 simplify to?
What does the inequality -p - 4p > -10 simplify to?
When graphing z < 7, would you use an open or closed circle?
When graphing z < 7, would you use an open or closed circle?
What is the solution to 6x + 10 > 5x - 12?
What is the solution to 6x + 10 > 5x - 12?
What is the inequality represented by -3 - 6(4x + 6) > -111?
What is the inequality represented by -3 - 6(4x + 6) > -111?
What does the inequality 4(2a + 3) < 3(a - 1) simplify to?
What does the inequality 4(2a + 3) < 3(a - 1) simplify to?
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Study Notes
Inequalities and Graphing
- The inequality x ≤ 24 indicates that x can take any value less than or equal to 24.
- An open circle is used when graphing b < 6, indicating that b cannot equal 6.
- The inequality 9 ≥ -2m + 2 - 3 can be simplified to m ≥ -5.
- For the inequality 3(x - 2) < 2(x + 9), it results in x < 250.
- The statement s ≤ 18 expresses that the number of students is at most 18.
Graphing with Open and Closed Circles
- When graphing m ≤ 5, a closed circle is used to represent that m can equal 5.
- Similarly, an open circle is used when graphing x > -14, indicating x cannot equal -14.
- The inequality z < 7 is represented by an open circle, meaning z cannot equal 7.
Solving Inequalities
- To solve the inequality 12 ≥ 15 - 6y, the solution is y ≥ ½.
- For financial constraints, the inequality to determine monthly payments after a $400 down payment is 12x + 400 < 1200.
- The inequality -p - 4p > -10 simplifies to p < 2.
- The inequality 6x + 10 > 5x - 12 can be solved to show x > -22.
- The inequality -3 − 6(4x + 6) > -111 results in x < 3.
Multi-step Inequalities
- Solving 4(2a + 3) < 3(a - 1) provides understanding of operations involving variables and constants.
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