Unit 4: Solving Linear Equations & Inequalities · AI-A.CED.1, AI-A.REI.3, AI-A.REI.12
Algebra I Regents
Notes
The flip rule. From −2x > 8, divide by −2 and flip: x < −4. Check with a number: x = −5 works because −2(−5) = 10 > 8.
Vocabulary
half-plane: The set of points on one side of a boundary line, used to graph a two-variable inequality.
Practice (no calculator unless marked)
Solve 5(x − 2) ≤ 3x + 20 algebraically. Enter the solution as an inequality in x.
A tour bus can seat at most 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If a is adult tickets and c is child tickets, which system models a profit?
A. a + c < 48 and 18a + 12c > 650
B. a + c ≤ 48 and 18a + 12c ≥ 650
C. a + c < 48 and 18a + 12c < 650
D. a + c ≤ 48 and 18a + 12c ≤ 650
Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. Which inequality could be used to determine the number of dimes, d, she needs?
A. 1.75 + d ≥ 3.00
B. 1.75 + 0.10d ≥ 3.00
C. 1.75 + d ≤ 3.00
D. 1.75 + 0.10d ≤ 3.00
Solve 5(x − 2) ≤ 3x + 20 algebraically. Enter the solution as an inequality in x.
A tour bus can seat at most 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If a is adult tickets and c is child tickets, which system models a profit?
A. a + c < 48 and 18a + 12c > 650
B. a + c ≤ 48 and 18a + 12c ≥ 650
C. a + c < 48 and 18a + 12c < 650
D. a + c ≤ 48 and 18a + 12c ≤ 650
Ashley only has 7 quarters and some dimes in her purse. She needs at least $3.00 to pay for lunch. Which inequality could be used to determine the number of dimes, d, she needs?
A. 1.75 + d ≥ 3.00
B. 1.75 + 0.10d ≥ 3.00
C. 1.75 + d ≤ 3.00
D. 1.75 + 0.10d ≤ 3.00
Solve 5(x − 2) ≤ 3x + 20 algebraically. Enter the solution as an inequality in x.
A tour bus can seat at most 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If a is adult tickets and c is child tickets, which system models a profit?