Year 8 Solving Equations Term 3

One-Step Equations

100

4 = -8 + x

x= 12

200

x + 12 = 0

x= -12

300

3 = -2 – x

x= -5

400

5x = -80

x= -16

500

-16 = x+2

x= -18

Two-Step Equations

100

6x – 13 = 11

x= 4

200

3x + 5 = 14

x= 3

300

x/2 -3=-8

x= -10

400

x/2-50=10

x= 120

500

x/3+16=-3

x= -57

Distributive Property Equations

100

Solving Equations

-(-x + 2) = 6

x = 8

200

Solving Equations

-3(p + 4) = 6

p = -6

300

Solving Equations

2(n+5) = 4

n = -3

400

Solving Equations

5(m-3) = 4

m = 19/5

or  3 4/5 

500

Solving Equations

3(𝑥 − 9) = −3

x = 8

Multi-Step Equations

100

Solving Equations

1(3x + 4x) = 7

x = 1

200

Solving Equations

2(4 + 5x) = 58

x = 5

300

Solving Equations

-45 = 7x + 4 

x = -7

400

Solving Equations

14 = 1(3a + 8)

a=2

500

Solving Equations

-21 = 7(5k - 8)

k = 1

Random

100

How many Platonic Solids are there ?

What are their names? 

5

Tetrahedron         Hexahedron

Octahedron.         Icosahedron

Dodecahedron

200

What is the defining mathematical property that all faces of a Platonic solid must share?

 They must be congruent (identical) regular polygons 

300

Which ancient Greek philosopher is famously associated with these shapes, though they were studied earlier?

What five elements match the shapes ? 

Plato

Tetrahedron - Fire         Hexahedron - Earth 

Octahedron - Air.          Icosahedron - Water 

Dodecahedron - Cosmos?Universe or Aether 

400

Plato assigned Air to the octahedron and Water to the icosahedron. What physical property did these two share with Fire to allow them to transform into each other?

They are all composed of the same basic triangular building blocks (equilateral triangles).

500

What is the name of Johannes Kepler’s 1596 astronomical treatise where he proposed that the distance relationships between the planets could be explained by nesting the five Platonic solids inside celestial spheres?

Mysterium Cosmographicum 

(The Cosmographic Mystery).