# Using distributive property :Solve and check the solution

 1)3+4(z+5)=31   2)14+2(4g-3)=40   3)5m+2(m+1)=23   4)5h+2(11-h)=-5   5)3c-3(6-2c)=27

reshown Dec 26, 2012

1).Solve and check the solution 3+4(z+5)=31.

Given equation is 3+4(z+5)=31

Apply distributive property: a(b+c) = ab + ac

3+4*z+4*5 = 31

3+4z+20 = 31

4z+23 = 31

Subtract 23 from each side

4z+23-23 = 31-23

4z = 8

Divide each side by 4

4z/4 = 8/4

z = 2.

Check solution:-

Substitute z = 2 in equation 3+4(z+5)=31

3+4(2+5) = 31

3+4(7) = 31

3+28 = 31

31 = 31

The equation is true.

5) 3c-3(6-2c)=27

Apply distributive property a(b-c) = ab - ac

3c-3(6)+3(2c) = 27

3c-18+6c = 27

9c-18 = 27

9c-18+18 = 27+18

9c = 27+18

9c = 45

Divide each side by 9

9c/9 = 45/9

c = 5

Check:

Substitute c = 5 in origional solution 3c-3(6-2c)=27

3(5)-3(6-2(5)) = 27

15-3(6-10) = 27

15-3(-4) = 27

15+12 = 27

27 = 27

The equality is correct.

The value of c is 5.

2 ) solve and check solution 14+2(4g-3)=40

The equation is 14 + 2 (4g - 3) = 40

Apply distributive property a ( b + c ) = ab + ac

14 + 2(4g) +2 ( -3) = 40

14 + 8g - 6 = 40

8g + 8 = 40

Subtract 8 from each side

8g + 8 - 8 = 40 - 8

8g = 40 - 8

8g = 32

Divide each side by 8

g = 32 / 8

g = 4

Check solution:-

Substitute g = 4 in equation 14 + 2 (4g - 3) = 40

14 + 2 ( 4 (4) - 3 ) = 40

14 + 2 ( 16 -3 ) = 40

14 + 2 ( 13 ) = 40

14 + 26 = 40

40 = 40

The equation is true

The solution is g = 4

3)solve and check the solution 5m+2(m+1)=23

Given equation is 5m+2(m+1)=23

Apply  distributive property;a(b+c)=ab+ac

5m+2*m+2*1=23

5m+2m+2=23

7m+2=23

Subtrct 23 from each side

7m+2-23=23-23

7m-21=0

7m-21+21=0+21

7m=21

Divide each side by 7

7m/7=21/7

m=3

Check solution:-

Substitinute m=3 in 5m+2(m+1)=23

5*3+2(3+1)=23

15+2(4)=23

15+8=23

23=23

4) 5h + 2(11-h) = -5

Apply distributive property a (b-c) = ab-ac

5h + 2(11) - 2(h) = -5       [distribute 2]

5h + 22 - 2h = -5

Subtract 22 from each side

5h + 22 - 2h - 22 = -5 -22

5h - 2h = -27

3h = -27

divide each side by 3

h = - 9

The solution is h = -9

check solution:

Substitute h = -9 in 5h + 2(11-h) = -5

5(-9) + 2(11-(-9)) = -5

-45 + 2 (11+9) = -5

-45 + 2 (20) = -5

-45 + 40 = -5

-5 = -5

The solution have been checked