Algebraic Concepts Flashcards

What is the solution to the inequality 4x < 20?

Answer: x < 5

Divide both sides by 4: x < 5.

Which ordered pair lies on the line y = 2x - 1?

Answer: (0, -1)

When x = 0: y = 2(0) - 1 = -1, confirming (0, -1) is on the line.

Evaluate the expression 2a² - 3b when a = 3 and b = 4.

Answer: 6

Substitute: 2(3²) - 3(4) = 2(9) - 12 = 18 - 12 = 6.

Which property is used to rewrite 5(x + 3) as 5x + 15?

Answer: Distributive property

The distributive property states a(b + c) = ab + ac, used here to expand 5(x + 3).

Solve for x: x/4 + 3 = 7

Answer: 16

Subtract 3 from both sides: x/4 = 4, then multiply both sides by 4: x = 16.

Two numbers have a sum of 20 and a difference of 6. What are the two numbers?

Answer: 7 and 13

If x + y = 20 and x - y = 6, adding gives 2x = 26, so x = 13 and y = 7.

What does it mean when two linear equations have no solution?

Answer: The lines are parallel

Parallel lines never intersect, so a system of two parallel lines has no solution.