PA-U2.1 Lesson Check: One-Step Equations

Pairs of operations that undo each other

• inverse operations

• solution

• inequality

Answer explanation

Inverse operations are pairs of operations that cancel each other out, such as addition and subtraction or multiplication and division. This makes 'inverse operations' the correct choice for pairs of operations that undo each other.

Tags

CCSS.6.EE.A.4

A number increased by 7 equals 15. What is the number?

• 6

• 8

• 7

• 5

Answer explanation

To find the number, set up the equation: x + 7 = 15. Subtract 7 from both sides: x = 15 - 7, which simplifies to x = 8. Therefore, the number is 8.

Tags

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

Translate the following sentence into an equation: "Five less than a number is 12."

Answer explanation

The phrase 'Five less than a number' translates to 'x - 5'. Setting this equal to 12 gives the equation 'x - 5 = 12', which is the correct choice.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.6

CCSS.6.EE.B.7

• Addition

• Subtraction

• Multiplication

• Division

Answer explanation

To isolate x in the equation x + 9 = 20, we need to eliminate the +9. This is done by performing the opposite operation, which is subtraction. Therefore, we subtract 9 from both sides, leading to the correct choice: Subtraction.

Tags

CCSS.6.EE.B.7

Ethan has $10 and he spends $4 on a snack. How much money does Ethan have left?

• 6

• 14

• 10

• 4

Answer explanation

Ethan starts with $10 and spends $4 on a snack. To find out how much he has left, subtract the amount spent from the initial amount: 10 - 4 = 6. Therefore, Ethan has $6 left.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.NS.B.3

Answer explanation

Sarah has x dollars, spends 5, and has 20 left. This can be represented as x - 5 = 20, which shows the amount left after spending. The correct equation is x - 5 = 20.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.6

CCSS.6.EE.B.7

David has 3 packs of pencils, each containing the same number of pencils. In total, he has 21 pencils. How many pencils are in each pack?

• 7

• 6

• 8

• 9

Answer explanation

David has 21 pencils divided into 3 packs. To find the number of pencils per pack, divide 21 by 3. 21 ÷ 3 = 7. Therefore, each pack contains 7 pencils.

Tags

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.NS.B.2

• Yes

• No

Answer explanation

To check if x = 4 is a solution, substitute 4 into the equation: 4 + 3 = 7. Since this is true, x = 4 is indeed a solution. Therefore, the answer is Yes.

Tags

CCSS.6.EE.B.5

CCSS.6.EE.B.7

Translate the following sentence into an equation: "The product of a number and 6 is 42."

Answer explanation

The phrase 'The product of a number and 6' indicates multiplication, which can be represented as '6x'. Setting this equal to 42 gives the equation '6x = 42', making this the correct choice.

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.6

CCSS.6.EE.B.7

Translate the following sentence into an equation: "The sum of a number and 9 is 17."

Answer explanation

The phrase 'The sum of a number and 9' translates to 'x + 9'. The sentence states that this sum equals 17, leading to the equation 'x + 9 = 17', which is the correct choice.

Tags

CCSS.6.EE.B.6

CCSS.6.EE.B.7