Algebra and Patterns Flashcards

Solve for x: 3x + 7 = 22

Answer: x = 5

Subtract 7 to get 3x = 15, then divide by 3 to get x = 5.

What is the next number in the pattern 2, 6, 18, 54, ...?

Answer: 162

Each term is multiplied by 3, so 54 × 3 = 162.

Evaluate 4a − 2b when a = 3 and b = 5.

Answer: 2

4(3) − 2(5) = 12 − 10 = 2.

Which expression represents "7 less than twice a number n"?

Answer: 2n − 7

Twice a number is 2n, and 7 less than that means subtracting 7 from 2n.

Solve for x: x/4 − 3 = 5

Answer: x = 32

Add 3 to get x/4 = 8, then multiply by 4 to get x = 32.

Simplify: 5x + 3 − 2x + 8

Answer: 3x + 11

Combine x-terms (5x − 2x = 3x) and constants (3 + 8 = 11).

Which inequality is the solution to 2x − 5 > 9?

Answer: x > 7

Add 5 to get 2x > 14, then divide by 2 to get x > 7.

In the arithmetic sequence 7, 11, 15, 19, ..., what is the 10th term?

Answer: 43

The 10th term is 7 + 9(4) = 43.

A table shows x-values 1, 2, 3, 4 paired with y-values 5, 8, 11, 14. Which rule fits the table?

Answer: y = 3x + 2

y increases by 3 each time, and 3(1) + 2 = 5 matches the first pair.

What is the slope of the line through the points (2, 3) and (6, 11)?

Answer: 2

Slope = (11 − 3) / (6 − 2) = 8/4 = 2.

What is the next number in the pattern 1, 4, 9, 16, 25, ...?

Answer: 36

These are perfect squares, so the next is 6² = 36.

A gym charges a $25 sign-up fee plus $15 per month. Which expression gives the total cost for m months?

Answer: 25 + 15m

The one-time fee is constant (25) and the monthly charge multiplies by m (15m).

If f(x) = x² − 3x, what is f(4)?

Answer: 4

f(4) = 16 − 12 = 4.

Solve for x: 5(x − 2) = 3x + 4

Answer: x = 7

5x − 10 = 3x + 4 gives 2x = 14, so x = 7.

Which ordered pair (x, y) solves the system x + y = 10 and x − y = 4?

Answer: (7, 3)

Adding the equations gives 2x = 14, so x = 7 and y = 3.

Solve the proportion 3/8 = x/40.

Answer: x = 15

Since 40 = 8 × 5, x = 3 × 5 = 15.

The sum of three consecutive integers is 48. What is the smallest integer?

Answer: 15

n + (n + 1) + (n + 2) = 48 gives 3n = 45, so n = 15.

What value of x makes 2x + 3 = 3x − 4 true?

Answer: x = 7

Subtract 2x and add 4 to both sides to get x = 7.

A pattern repeats: triangle, square, circle, triangle, square, circle, ... What is the 20th shape?

Answer: Square

20 ÷ 3 leaves a remainder of 2, so the 20th shape is the 2nd in the cycle, a square.

Which expression is equivalent to −3(2x − 5)?

Answer: −6x + 15

−3 × 2x = −6x and −3 × −5 = +15.