Algebraic Proofs Practice

Properties 1

100

6y=6y

Reflexive Property

200

If a=-5, then 2a=-10

Multiplication Property

300

If 4w-1=11, then 4w=12

Addition Property

400

If 5k=-25, then 5k-1=-25-1

Subtraction Property

500

If 4m+n=7 and n=3, then 4m+3=7

Substitution Property

Properties 2

100

If -8q=-56, then q=7

Division Property

200

If 3x=y, then y=3x

Symmetric Property

300

-3(2x-5)=-6x+15

Distributive Property

400

If 4x=8, then 4x/m=8/m

Division Property

500

If a+b=c and c=d, then a+b=d

Transitive Property

Proofs 1

100

Given -5x+2=-28, Prove: x=6 (Hint 3 rows)

1. -5x+2=-28 Given

2. -5x=-30 Subtraction Property

3. x=6 Division Property

200

Given: 19=−37+8x, Prove: x=7 (hint: 4 rows)

1. 19=-37+8x Given

2. 56=8x Addition Property

3. 7=x Division Property

4. x=7 Symmetric Property

300

Given: −8x+5=−6x+3, Prove: x=1

1. −8x+5=−6x+3 Given

2. −8x= −6x−2 Subtraction Property

3. -2x=-2 Addition Property

4. x=1 Division Property

400

Given: −2(−5x−1)+5x−3=−31, Prove: x=-2

1. −2(−5x−1)+5x−3=−31 Given

2. 10x+2+5x-3=-31 Distribution Property

3. 15x-1=-31 Addition Property

4. 15x=-30 Addition Property

5. x=-2 Division Property

500

Given: 17-3(w+5)=6(w+5)-2w, Prove: w=-4

1. 17-3(w+5)=6(w+5)-2w Given

2. 17-3w-15=6w+30-2w Distributive Property

3. 2-3w=4w+30 Subtraction Property

4. 2-7w=30 Subtraction Property

5. -7w=28 Subtraction Property

6. w=-4 Division Property

Proofs 2

100

Given: 42+9b=42, Prove: b=0 (hint 3 rows)

1. 42+9b=42 Given

2. 9b=0 Subtraction Property

3. b=0 Division Property

200

Given: 79=5a+9 Prove: a=14 (hint 4 rows)

1. 79=5a+9 Given

2. 70=5a Subtraction Property

3. 14=a Division Property

4. a=14 Symmetric Property

300

Given: 14x−9=10x+3, Prove: x=3

1. 14x−9=10x+3 Given

2. 4x-9=3 Subtraction Property

3. 4x=12 Addition Property

4. x=3 Division Property

400

Given: −2(−3x+5)−3x+1=15, Prove: x=8

1. −2(−3x+5)−3x+1=15 Given

2. 6x-10-3x+1=15 Distributive Property

3. 3x-9=15 Addition/Subtraction Property

4. 3x=24 Addition Property

5. x=8 Division Property

500

Given: −(2x−6)+10x=−5x−2(−7x−7)

Prove: x=-8

1. −(2x−6)+10x=−5x−2(−7x−7) Given

2. -2x+6+10x=-5x+14x+14 Distributive Property

3. 8x+6=9x+14 Addition Property

4. -1x+6=14 Subtraction Property

5. -x=8 Subtraction Property

6. x=-8 Division Property

Random Trivia

100

Which author wrote "Green Eggs and Ham"?

Dr. Seuss 

200

What is the princess' name from Beauty and the Beast?

Belle

300

How many sides does a stop sign have?

8

400

On a standard traffic light, is the green light on the top or bottom?

Bottom

500

What does a²+b²=c² called?

Pythagorean Theorem