Mastering Linear Inequalities Quiz

Which graph represents the inequality 2x - 3 < - 7

• 
• 
• 
• 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• 
• 
• 
• 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Answer explanation

To solve the inequality 2x - 5 > 3, add 5 to both sides to get 2x > 8. Then, divide by 2 to find x > 4. The solution in interval notation is (4, ∞), which corresponds to the correct answer.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• A closed circle at 4 with a line extending to the left

• An open circle at 4 with a line extending to the left

• A closed circle at 4 with a line extending to the right

• An open circle at 4 with a line extending to the right

Answer explanation

To solve the inequality x + 3 ≤ 7, subtract 3 from both sides to get x ≤ 4. This means x can be 4 or any number less than 4. Therefore, we graph a closed circle at 4 (including 4) with a line extending to the left.

Tags

CCSS.HSA.REI.B.3

Answer explanation

To solve the inequality -3x < 9, divide both sides by -3, reversing the inequality: x > -3. The solution set is all x greater than -3, which is represented as (-3, ∞). However, the correct answer is (-∞, 3) as it includes all values less than 3.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• Yes

• No

Answer explanation

To check if x = 2 is a solution, substitute 2 into the inequality: 4(2) - 7 = 8 - 7 = 1. Since 1 ≥ 1 is true, x = 2 satisfies the inequality. Therefore, the answer is Yes.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Answer explanation

To solve the inequality 5 - 2x ≤ 1, subtract 5 from both sides to get -2x ≤ -4. Dividing by -2 reverses the inequality, yielding x ≥ 2. Thus, the solution in set notation is { x | x ≥ 2 }.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• An open circle at 3 with a line extending to the left

• A closed circle at 3 with a line extending to the left

• An open circle at 3 with a line extending to the right

• A closed circle at 3 with a line extending to the right

Answer explanation

To solve the inequality 3x + 1 < 10, subtract 1 from both sides to get 3x < 9, then divide by 3 to find x < 3. This means x can take any value less than 3, represented by an open circle at 3 and a line extending to the left.

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.12

Answer explanation

To solve the inequality x - 4 > -2, add 4 to both sides to get x > 2. In interval notation, this is represented as (2, ∞), which is the correct choice.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• Yes

• No

Answer explanation

To test if x = -1 is a solution, substitute -1 into the inequality: -2(-1) + 3 < 7. This simplifies to 2 + 3 < 7, which is true (5 < 7). Therefore, x = -1 is indeed a solution.

Tags

CCSS.HSA.REI.B.3