Question

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Answer 1

Answer:

Statement                                                Reason

$\frac{1}{2}(10m-14)+9=12$                       Given

$5m-7+9=12$                                Distributive property

$5m+2=12$                                   Combine like terms

$5m=10$                                       Subtraction property of equality

$m=2$                                           Division property of equality

Step-by-step explanation:

The given equation is

$\frac{1}{2}(10m-14)+9=12$

We need to prove m=2.

$\frac{1}{2}(10m)+\frac{1}{2}(-14)+9=12$                          (Distributive property)

$5m-7+9=12$

$5m+2=12$                               ( Combine like terms)

Subtract 2 from both sides.

$5m=12-2$                     (Subtraction property of equality)

$5m=10$

Divide both sides by 5.

$\frac{5m}{5}=\frac{10}{5}$

$m=2$                       (Division property of equality)

Hence proved.

Answer 2

1. $\frac{1}{2}$(10m - 14) + 9 = 12        1. Given

2.    5m - 7 + 9 = 12          2. Distributive Property

3.    5m      + 2 = 12          3. Simplify (added like terms)

4.    5m            = 10          4. Subtraction Property of Equality

5.      m            =  2           5. Division Property of Equality