Solving equations using properties?

Question

Solve (k/0.2) - 3 = 7
(M/3) + 5.9 =6
(n/10) + 3 = 5.4

Answer 1

a)    (k/0.2) - 3 = 7

      Add 3 to each side

     (k/0.2) - 3 + 3 = 7 + 3

     Apply additive inverse property a+(-a)=0

     (k/0.2) = 10

     Multiply each side by 0.2

    (0.2)(k/0.2) = 0.2 * 10

    Cancel common terms

      k = 2

b)    (M/3) + 5.9 =6

       Subtract  5.9  from each side

      (M/3) + 5.9 - 5.9 = 6 - 5.9

       Apply additive inverse property a+(-a)=0

       (M/3) = 0.1

       Multiply each side by 3

      (3)(M/3)=(3) (0.1)

      Cancel common terms

       M = 0.3

     

c)  (n/10) + 3 = 5.4

      Subtract  3  from each side

      ( n/10) + 3 - 3 = 5.4 - 3

      Apply additive inverse property a+(-a)=0

      (n/10) = 2.4

     Multiply each side by 10

     (10)(n/10)= 10 * 2.4

     Cancel common terms

     n = 24

    The values of k,m and n are 2, 0.3 and 24 respectively

Answer 2

1) The equation is .

Apply Addition Property of Equality: .

Add 3 to each side.

Apply Additive Inverse Property: .

Apply Additive Identity Property: .

Add 7 and 3.

Apply Multiplication Property of Equality: .

Cancel common terms.

Multiply 10 and 0.2.

is the solution.

Answer 3

2) The equation is .

Apply Subtraction Property of Equality: .

Subtract 5.9 from each side.

Apply Additive Inverse Property: .

Apply Additive Identity Property: .

Subtract 5.9 from 6.

Apply Multiplication Property of Equality: .

Cancel common terms.

Multiply 0.1 and 3.

is the solution.

Answer 4

3) The equation is .

Apply Subtraction Property of Equality: .

Subtract 3 from each side.

Apply Additive Inverse Property: .

Apply Additive Identity Property: .

Subtract 3 from 5.4.

Apply Multiplication Property of Equality: .

Cancel common terms.

Multiply 2.4 and 10.

is the solution.