Expressions and Equations Flashcards

Which expression is equivalent to 3(2x + 4)?

Answer: 6x + 12

Applying the distributive property: 3 × 2x = 6x and 3 × 4 = 12, giving 6x + 12.

Solve for x: x + 9 = 21

Answer: x = 12

Subtracting 9 from both sides: x = 21 − 9 = 12.

Which property justifies the step: 4x + 3x = (4 + 3)x?

Answer: Distributive Property

The Distributive Property allows factoring out a common variable: 4x + 3x = (4 + 3)x = 7x.

What is the value of 5n − 3 when n = 4?

Answer: 17

Substituting n = 4: 5(4) − 3 = 20 − 3 = 17.

Which inequality represents 'a number decreased by 5 is at least 10'?

Answer: n − 5 ≥ 10

'Decreased by 5' means subtraction, and 'at least 10' means greater than or equal to 10, giving n − 5 ≥ 10.

Solve for y: 3y = 36

Answer: y = 12

Dividing both sides by 3: y = 36 ÷ 3 = 12.

Which expression represents 'seven less than twice a number p'?

Answer: 2p − 7

'Twice a number p' is 2p, and 'seven less than' means subtract 7 from it, giving 2p − 7.