4. the weight of abes dog can be found using the expression 2(x + 3), where x is the number of weeks. the…

4. the weight of abes dog can be found using the expression 2(x + 3), where x is the number of weeks. the weight of karens dog can be found using the expression 3(x + 1), where x is the number of weeks. will the dogs ever be the same weight? explain.

4. the weight of abes dog can be found using the expression 2(x + 3), where x is the number of weeks. the weight of karens dog can be found using the expression 3(x + 1), where x is the number of weeks. will the dogs ever be the same weight? explain.

Answer

Explanation:

Step1: Set the two expressions equal

Set (2(x + 3)=3(x + 1)) since we want to find when the weights are the same.

Step2: Expand both sides

Expand the left - hand side: (2(x + 3)=2x+6). Expand the right - hand side: (3(x + 1)=3x + 3). So we have (2x+6 = 3x+3).

Step3: Solve for x

Subtract (2x) from both sides: (2x+6-2x=3x + 3-2x), which gives (6=x + 3). Then subtract 3 from both sides: (6-3=x+3 - 3), so (x = 3).

Answer:

Yes, the dogs will have the same weight after 3 weeks. When (x = 3), the weight of Abe's dog is (2(3 + 3)=2\times6 = 12), and the weight of Karen's dog is (3(3+1)=3\times4 = 12).