Complete the following proof. Given: 200 = 4m + 18 – 2m Prove: m = 91 Statements Reason 1. 200 = 4m + 18 – 2m 1. Given 2. 200 = 2m + 18 3. 182 = 2m 4. 91 = m 5. m = 91

Question

Complete the following proof.

Given: 200 = 4m + 18 – 2m

Prove: m = 91

 

Statements	Reason
1. 200 = 4m + 18 – 2m	1. Given
2. 200 = 2m + 18	2. Symmetric Property of EqualityAddition Property of EqualityCombining Like TermsReflexive Property of EqualityDivision Property of EqualitySubtraction Property of Equality
3. 182 = 2m	3. Division Property of EqualityCombining Like TermsSymmetric Property of EqualityReflexive Property of EqualityAddition Property of EqualitySubtraction Property of Equality
4. 91 = m	4. Subtraction Property of EqualityDivision Property of EqualityCombining Like TermsReflexive Property of EqualityAddition Property of EqualitySymmetric Property of Equality
5. m = 91

Answer 1

1) Given: 200= 4m + 18 -2m

2) Combining Like Terms (4m-2m = 2m)

3) Subtraction property of equality (200-18 = 2m + 18 -18)

4) Division property of equality (182/2 = 2m/2)

5) Symmertric property of equality (91=m => m= 91)

Answer 2

 

You have answered your own question! The reasoning is correct.

200=4m+18-2m, 

200=2m+18 (combine like terms on the right-hand side).

Subtract 18 from each side (maintaining equality by taking equal amounts from each side):

182=2m,

Divide each side by 2 (maintaining equality by dividing by an equal amount on each side):

91=m which can also be written m=91 because the amounts on either side are equal.