Algebraic Proofs Practice

Fill in the missing steps

h

g

f

e

Distributive Prop

x = 7

Addition Prop

4x = 28

4x + 8 - 8 = 36 - 8

Prove

Simplify

Division Prop

Tags

CCSS.HSA.REI.A.1

Given: 5(x+2) = -3x-6

Prove: x = -2

a

b

c

d

e

f

g

h

i

j

Subtraction Property

8x+10 = -6

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

5x+10 = -3x-6

Distributive Property

Addition Property

Division Property

Given

x = -2

8x = -16

Tags

CCSS.8.EE.C.7B

Given: 4x+9 = 16-3x

Prove: x = 1

a

b

c

d

e

f

g

h

7x+9 = 16

Division Property

x = 1

Given

Addition Property

Subtraction Property

Distributive Property

4x+9 = 16-3x

7x = 7

Multiplication Property

Tags

CCSS.HSA.REI.A.1

a

b

c

d

e

f

g

h

i

j

Subtraction Property

7x+14 = 11

7x = -3

Division Property

Addition Property

4+6x+10 = 11-x

6x+14 = 11-x

Simplify

x = -3/7

Distributive Property

Tags

CCSS.HSA.REI.A.1

a

b

c

d

e

f

g

h

x = 6

Subtraction Property

Simplify

Division Property

-5x+2 = -28

-5x = -30

Given

Multiplication Property

Addition Property

Tags

G.CO.C

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

Prove: w = -4

a

b

c

d

e

f

g

h

i

j

-7w = 28

w = -4

-7w+2 = 30

Distributive Property

Subtraction Property

Division Property

-3x+2 = 4w+30

Subtraction Property #2

17-3w-15 = 6w+30-2w

Simplify

Tags

G.CO.C

Fill in the proof.

Given: 3(2x - 6) = x + 7

Prove: x = 5

j

i

g

h

f

e

d

c

b

a

3(2x - 6) = x + 7

Distributive

x = 5

5x - 18 = 7

Subtraction

Division

5x = 25

6x - 18 = x + 7

Given

Addition

Tags

CCSS.HSA.REI.A.1

Given: 3x+12 = 8x-18

Prove: x = 6

a

b

c

d

e

f

g

h

i

j

Division Property

12 = 5x-18

Subtraction Property

3x+12 = 8x-18

30= 5x

6 = x

Given

x = 6

Addition Property

Symmetric Property

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Given: 3(5x+1) = 13x+5

Prove: x = 1

a

b

c

d

e

f

g

h

i

j

x = 1

Distributive Property

15x+3 = 13x+5

3(5x+1) = 13x+5

Subtraction Property #2

2x = 2

2x+3 = 5

Division Property

Given

Subtraction Property

Tags

CCSS.HSA.REI.A.1

Given: 7y-84 = 2y+61

Prove: y = 29

a

b

c

d

e

f

g

h

Addition Property

y = 29

Distributive Property

7y-84 = 2y+61

Division Property

5y = 23

5y-84 = 61

Subtraction Property

Given

5y = 145

Tags

CCSS.6.EE.A.2

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7