Properties 1
If -5x-1=-11 then -5x=-10
Addition Property
If 6y+3=24 then 6y=21
Subtraction Property
Given: (5y-1)/2=7 Prove: y=3
1. (5y-1)/2=7
2. 5y-1=14
3. 5y=15
4.y=3
1. Given
2. Multiplication Property
3. Addition Property
4. Division property
Given: 10k-4=2k-20 Prove: k=-2
1. Given
2. Addition Property
3. Subtraction Property
4. Division Property
1. 10k-4=2k-20
2. 10k=2k-16
3. 8k=-16
4. k=-2
Given: 4d=1/3(c-d) Prove: c=13d
1. 4d=1/3(c-d) 1. Given
2. 12d=c-d 2. Multiplication Property
3. 13d=c 3. Addition Property
4. c=13d 4. Symmetric Property
If 8x/2=4 then 8x=8
Multiplication Property
If 7x=21 then x=3
Division Property
Given: -8(w+1)=-5(w+10) Prove:w=14
1. -8(w+1)=-5(w+10)
2. -8w-8=-5w-50
3. -8w=-5w-42
4. -3w=-42
5. w=14
1. Given
2. Distributive Property
3. Addition Property
4. Addition Property
5. Division Property
Given: 8(x-1)=5x-35 Prove: x=-9
1. Given
2. Distributive Property
3. Subtraction Property
4. Addition Property
5. Division Property
1. 8(x-1)=5x-35
2.
3.
4.
5. x=-9
If 6(4-x)=3(5+x) then 24-6x=15+3x
Distributive Property
If 7x+3x-2=4-1+5x then 10x-2=3+5x
Simplify
Given: 14-2(x+8)=5x-(3x-34) Prove: x=-9
1. 14-2(x+8)=5x-(3x-34)
2. 14-2x-16=5x-3x+34
3. -2x-2=2x+34
4. -2x=2x+36
5. -4x=36
6.x=-9
1. Given
2. Distributive Property
3. Simplify
4. Addition Property
5. Subtraction Property
6. Division Property
27+3x=27+3x
Reflexive Property
If 8x=24 then 24=8x
Symmetric Property
If 21x-5=2 and 8x+3=2 then 21x-5=8x+3
Transitive Property
If z=5 and 4x+3z=23 the 4x+15=23
Substitution Property