Solving Two-Step Equations Quiz

Answer explanation

To solve for x in the equation 3x + 5 = 14, subtract 5 from both sides to get 3x = 9. Then, divide both sides by 3 to find x = 3. Thus, the correct answer is x = 3.

Tags

CCSS.7.EE.B.4A

• Yes

• No

Answer explanation

To check if x = 2 is a solution, substitute into the inequality: 4(2) - 3 > 5, which simplifies to 8 - 3 > 5, or 5 > 5. This is false, so x = 2 is not a solution. Therefore, the answer is No.

Tags

CCSS.6.EE.B.5

• If you have 6 apples and you buy 2 more each day, how many days will it take to have 14 apples?

• You have 14 candies and you give away 2 each day. How many days until you have 6 left?

• You have 6 books and you buy 2 more each week. How many weeks until you have 14 books?

Answer explanation

The correct choice describes a scenario where you start with 6 books and buy 2 more each week, leading to the equation 2x + 6 = 14, where x represents the number of weeks needed to reach 14 books.

• A closed circle at 7, shading to the left

• An open circle at 7, shading to the left

• A closed circle at -1, shading to the right

• A closed circle at 7, shading to the right

Answer explanation

To solve the inequality x - 4 ≤ 3, add 4 to both sides to get x ≤ 7. This means x can be 7 or any number less than 7. On a number line, we represent this with a closed circle at 7 and shading to the left.

Tags

CCSS.7.EE.B.4B

Answer explanation

To solve the inequality 5x - 2 < 18, first add 2 to both sides: 5x < 20. Then, divide by 5: x < 4. Thus, the correct answer is x < 4.

Tags

CCSS.7.EE.B.4B

• Yes

• No

Answer explanation

To check if x = 5 is a solution, substitute 5 into the equation: 2(5) + 3 = 10 + 3 = 13. Since both sides equal 13, x = 5 is indeed a solution. Therefore, the answer is Yes.

Tags

CCSS.6.EE.B.5

• You have 11 dollars and you spend 3 dollars each day. How many days until you have 2 dollars left?

• You have 2 pencils and you buy 3 more each week. How many weeks until you have at least 11 pencils?

• You have 11 candies and you give away 3 each day. How many days until you have 2 left?

• You have 2 books and you buy 3 more each week. How many weeks until you have 11 books?

Answer explanation

The correct choice describes a situation where you start with 2 pencils and gain 3 each week, needing to reach at least 11. This translates to the inequality 3x + 2 ≥ 11, where x is the number of weeks.

Tags

CCSS.7.EE.B.4B

• A closed circle at 4

• An open circle at 4

• A closed circle at 14

• A closed circle at 9

Answer explanation

To solve the equation x + 5 = 9, subtract 5 from both sides to get x = 4. On a number line, this is represented by a closed circle at 4, indicating that 4 is included in the solution.

Tags

CCSS.7.EE.B.4B

Answer explanation

To solve for x in the equation 4x - 7 = 9, add 7 to both sides to get 4x = 16. Then, divide both sides by 4 to find x = 4. Thus, the correct answer is x = 4.

Tags

CCSS.7.EE.B.4A

• Yes

• No

Answer explanation

To check if x = 1 is a solution, substitute 1 into the inequality: 3(1) + 4 ≤ 7, which simplifies to 3 + 4 ≤ 7. This is true (7 ≤ 7), so x = 1 is indeed a solution. Therefore, the answer is Yes.

Tags

CCSS.6.EE.B.5