8th grade algebra

Example

Solve: 5x + 10 = 6x + 17

1. 5x + 10 = 6x + 17
2. −x + 10 = 17
3. −x = 7
4. x = −7

Answer: x = -7

Example

Simplify a³ × a⁹ and write it as a to a single power. What is the power?

1. a³ × a⁹ = a¹²

Answer: 12

Example

Does the point (5, 11) lie on the line y = 3x − 4?

1. y = 3 × 5 − 4 = 11
2. It matches, so yes.

Answer: Yes

Example

A line has slope −4 and crosses the y-axis at −8. Write its equation as y = … (type the right-hand side).

1. y = −4x − 8

Answer: -4x-8

Example

Solve the system: y = −2x + 1 and 3x + 2y = 4. Find x.

1. 3x + 2(−2x + 1) = 4
2. −x + 2 = 4
3. x = −2

Answer: x = -2

Example

Is this relation a function? {(5, 7), (−5, 0), (6, 7), (−2, 1)}

1. Every input has one output: yes.

Answer: Yes

Example

Find the nth term of the sequence 15, 13, 11, 9, …

1. Difference = −2
2. −2n + 17

Answer: -2n+17

Example

4⁹ × 4⁶ = 4ⁿ. What is n?

1. 9 + 6 = 15
2. 4⁹ × 4⁶ = 4¹⁵

Answer: 15

Example

6⁹ ÷ 6⁸ = 6ᵏ. What is k?

1. 9 − 8 = 1
2. 6¹

Answer: 1

Example

(9⁵)⁵ = 9ᵏ. What is k?

1. 5 × 5 = 25
2. 9²⁵

Answer: 25

Example

Write 8⁻³ as a fraction.

1. 8⁻³ = 1/8³ = 1/512

Answer: 1/512

Example

(x⁵ × x⁶) ÷ x⁴ = xᵏ. What is k?

1. 5 + 6 − 4 = 7

Answer: 7

Example

Solve: −6x − 1 = 2x − 17

1. −1 = 8x − 17
2. 16 = 8x
3. x = 2

Answer: x = 2

Example

Solve: 4(x + 4) = 2x + 8

1. 4x + 16 = 2x + 8
2. 2x = −8
3. x = −4

Answer: x = -4

Example

Solve: x/5 − 5 = x/10 − 4

1. 2x − 50 = x − 40
2. x = 10
3. x = 10

Answer: x = 10

Example

How many solutions does 2(x + 8) = 2x + 16 have?

1. 2x + 16 = 2x + 16
2. Infinitely many solutions

Answer: Infinitely many solutions

Example

Gym A charges $33 to join plus $3 per visit. Gym B charges $6 to join plus $6 per visit. For how many visits do they cost the same?

1. 33 − 6 = 6n − 3n
2. 27 = 3n
3. n = 9

Answer: 9

Example

x: 2, 5, 8, 11. y: −7, −16, −25, −34. What is the rate of change (slope)?

1. Δy = −9, Δx = 3
2. m = −9 ÷ 3 = −3

Answer: -3

Example

What kind of slope would the graph have? The temperature of a fridge held at exactly 4 °C all day, against time.

1. Zero

Answer: Zero

Example

What is the y-intercept of y = 4x − 9?

1. x = 0 → y = −9

Answer: -9

Example

Write the equation of the line with slope −5 and y-intercept 5. Type the right-hand side (y = …).

1. y = −5x + 5

Answer: -5x+5

Example

Find the equation of the line through (−1, 3) and (1, 11). Type the right-hand side (y = …).

1. m = 8 ÷ 2 = 4
2. 3 = 4 × (−1) + b → b = 7
3. y = 4x + 7

Answer: 4x+7

Example

x: 0, 1, 2, 3. y: −8, −13, −18, −23. Write y in terms of x. Type the right-hand side.

1. b = −8, m = −5
2. y = −5x − 8

Answer: -5x-8

Example

Find the slope of 3x + 6y = 18. Give a whole number or fraction.

1. 6y = −3x + 18
2. y = −(1/2)x + 3
3. m = −1/2

Answer: -1/2

Example

Where does y = −x + 4 cross the x-axis? Give the x-value.

1. −x = −4
2. x = 4

Answer: 4

Example

A bamboo shoot is 10 cm tall and grows 10 cm per day. In y = mx + b, what is b?

1. b = 10
2. y = 10x + 10

Answer: 10

Example

Is this relation a function? (2, −1), (6, −5), (−2, −5), (1, 6)

1. Every x appears once: it is a function.

Answer: Yes

Example

x: 0, 1, 2, 3, 4. y: 4, 5, 8, 13, 20. Is the function linear?

1. Differences: 1, 3, 5, 7
2. Not constant: nonlinear.

Answer: Nonlinear

Example

Liam's savings: y = 4x + 7. Zoe's savings (x = weeks): weeks 0, 1, 2, 3 → 4, 7, 10, 13. Who saves more per week?

1. Liam: 4 per week; Zoe: 3 per week
2. Liam

Answer: Liam

Example

Is (−5, 3) a solution of the system −2x + y = 13 and 2x + 4y = 2?

1. First: 13 ✓
2. Second: 2 ✓
3. Yes.

Answer: Yes

Example

Solve the system: y = x + 1 and 5x + 3y = 3. Type the solution like (2, −3).

1. 5x + 3(x + 1) = 3
2. 8x = 0 → x = 0
3. y = 1
4. (0, 1)

Answer: (0, 1)

Example

Solve: 4x + 3y = 9 and x − 3y = 6. Type the solution like (2, −3).

1. 5x = 15 → x = 3
2. 3y = 9 − 12 → y = −1
3. (3, −1)

Answer: (3, −1)

Example

How many solutions does the system y = −x + 1 and 2y = −2x + 2 have?

1. Infinitely many

Answer: Infinitely many

Example

At a museum, 5 adult and 5 child tickets cost $70. 4 adult and 2 child tickets cost $48. How much is one adult ticket? (Type the number only.)

1. c = 4
2. a = 10

Answer: 10