Solving Equations - Problems Workshop 2

Question 1

What is the factored form of b2 + 8b - 20?

Answer 1

(b + 10)(b - 2)

Question 2

What is the factored form of z2 - 64?

Answer 2

(z - 8)(z + 8)

Question 3

Factor the expression 4(x^2-3x-10)

Answer 3

4(x - 5)(x + 2)

Question 4

What is the factored form of 2x^2 + 8x - 154?

Answer 4

2(x - 7)(x + 11)

Question 5

Simplify the expression (12x - 8) / 4.

Answer 5

3x - 2

Question 6

Simplify the expression (6y - 4y2) / (2y2 - 3y).

Answer 6

-2

Question 7

What is the result of simplifying (x2 + 4x + 3) / (x + 1)?

Answer 7

x + 3

Question 8

What is the simplified result of (y2 - 25) / (y2 - 10y + 25 × y2 - 6y + 5)?

Answer 8

y + 5 / y + 1

Question 9

Solve for y in the equation 4y - 5 = y + 10.

Answer 9

y = 5

Question 10

What is the solution for x in the equation 7x + 7 = 2(x + 1)?

Answer 10

x = -1

Question 11

What is the solution for p in the equation p - 2 = 2(p - 1)?

Answer 11

p = 0

Question 12

What are the angles in a triangle if the first angle is x, the second is 2x, and the third is 3x?

Answer 12

30°, 60°, 90°

Question 13

What is the total distance traveled by Mary on the first day if she travels x km and 2x km on the second day for a total of 60 km?

Answer 13

20 km

Question 14

What is the gradient of a horizontal line?

Answer 14

0

Question 15

What is the gradient of the line y = (3/2)x - 3?

Answer 15

3/2

Question 16

What is the general equation of a straight line?

Answer 16

y = mx + b

Question 17

What is the equation of the line with a gradient of 2 passing through the point (0, 4)?

Answer 17

y = 2x + 4

Question 18

What are the solutions for the equations 2x + y = 8 and 3x - y = 7?

Answer 18

(3, 2)

Question 19

What is the solution for the equations 2x + 3y = 19 and 4x - y = 3?

Answer 19

(2, 5)

Question 20

What is the solution for the equations 2x - 3y = 5 and 5x + 2y = -16?

Answer 20

(-2, -3)

Question 21

What is the solution for the simultaneous equations a + c = 101 and 5a + 2c = 394?

Answer 21

a=64 and c=37

Question 22

Solve the equation x2 - 3x = 0.

Answer 22

x = 0 or x = 3

Question 23

Solve the equation x2 - 5x - 14 = 0.

Answer 23

x = 7 or x = -2

Question 24

What is the solution for the equation x2 + 4x + 1 = 0 using the quadratic formula?

Answer 24

x = -2 ± √3

Question 25

For the equation 3x² + 7x + 2 = 0, identify a, b, and c.

Answer 25

a = 3, b = 7, c = 2

Question 26

Solve for x in the equation 3x² + 7x + 2 = 0 using the quadratic formula.

Answer 26

x = −4±√12 / 2 = −2±√3

Question 27

For the equation x² + 3x + 4 = 0, identify a, b, and c.

Answer 27

a = 1, b = 3, c = 4

Question 28

Does the equation x² + 3x + 4 = 0 have real solutions?

Answer 28

No real solutions

Question 29

Factor the expression 6x+21

Answer 29

3(2x + 7)

Question 30

Factor the expression x^2+5x+6

Answer 30

(x + 3)(x + 2)

Question 31

Simplify the rational expression 9 - 6y / 24 - 16y.

Answer 31

3 / 8

Question 32

Simplify the expression (a² - 36) / (a - 6).

Answer 32

a + 6

Question 33

Simplify the expression (m² + 3m - 28) / (m² - 3m - 4).

Answer 33

m + 7 / (m + 1)

Question 34

What is the result of 14a - 12b / 6a + 3b ÷ 7a - 6b?

Answer 34

2 / 3

Question 35

Solve for z in the equation 2z / (z + 2) = 4.

Answer 35

z = -4

Question 36

Solve for x in the equation x - 3 / (x + 3) = 5.

Answer 36

x = -9 / 2

Question 37

What is the x-intercept when y = 0 in the equation 10x + 2y = 5?

Answer 37

x = 1/2

Question 38

What is the y-intercept when x = 0 in the equation 10x + 2y = 5?

Answer 38

y = 5/2

Question 39

What is the gradient of the line with equation y = 2x + 4?

Answer 39

2

Question 40

What is the equation of a line parallel to y = 2x + 4 that passes through the point (3, 4)?

Answer 40

y = 2x - 2

Question 41

Solve the system of equations: x + 2y = 10 and x - y = 1.

Answer 41

(x, y) = (4, 3)

Question 42

Solve the system of equations: x + y = 5 and 2x + y = 7.

Answer 42

(x, y) = (2, 3)

Question 43

Solve the system of equations: 2x + 3y = 8 and 3x - 2y = -7.

Answer 43

(x, y) = (-5/13, 38/13)

Question 44

What are the costs of a student and a teacher if 20s + 3t = 375 and 15s + 4t = 325?

Answer 44

s = 15, t = 25

Question 45

Solve the quadratic equation x² - x - 42 = 0.

Answer 45

x = 7 or x = -6

Question 46

Solve the quadratic equation 2x² + 3x + 1 = 0 using the quadratic formula.

Answer 46

x = -1/2, -1