Solve and check the solution

Question

Solve the equation.Check your solution

1) 12v+14+10v=80

2) 11w-9-7w=15

3) 5a+3-3a=-7

4) 6c-8-2c=-16

5)7z-13z-21=9

Answer 1

1)Given equation is 12v+14+10v = 80

22v+14 = 80

Apply subtraction property, subtract 14 from each sides

22v+14-14 = 80-14

22v = 66

Apply divisible property,divide by 22 each sides

22v/22 = 66/22

⇒v = 3

Check:

Substitute the value of v in given eqation.

12(3)+14+10(3) = 80

36+14+30 = 80

80 = 80

2)11w-9-7w = 15

4w-9 = 15

Apply addition property, add 9 to each sides

4w-9+9 = 15+9

4w = 24

Aplly division property, divide by4 to each sides

4w/4 = 24/4

⇒w = 6

Check:

substitute the value of w in eqation.

11(6)-9-7(6) = 15

66-9-42 = 15

66-51 = 15

15 = 15

3)5a+3-3a = -7

2a+3 = -7

Aplly subtraction property, subtract 3 from each sides.

2a+3-3 = -7-3

2a = -10

Aplly divisible property,divide by 2 each sides

2a/2 = -10/2

⇒a = -5

Check:

substitute the value of a ineqation.

5(-5)+3-3(-5) = -7

-25+3+15 = -7

-25+18 = -7

-7 = -7

4)6c-8-2c = -16

4c-8 = -16

Apply addition property,add 8 to each sides.

4c-8+8 = -16+8

4c = -8

Apply division property, divide by 4 to each sides.

4c/4 = -8/4

⇒c = -2

Check:

substitute the value of c in equation.

6(-2)-8-2(-2) = -16

-12-8+4 = -16

-20+4 = -16

-16 = -16

5)7z-13z-21 = 9

-6z-21 = 9

Apply addition property, add 21 to each sides.

-6z -21+21 = 9+21

-6z = 30

Aplly division property, divide by -6 each sides.

-6z/-6 = 30/-6

⇒z = -5

Check:

substitute the value of z in eqation.

7(-5)-13(-5)-21 = 9

-35+65-21 = 9

65-56 = 9

9 = 9