Question

Clare claims that 5x+2=20 has the same solution as 5(5x+2)=60. Kiran claims that 5x+2=12 has the same solution as 5(5x+2)=60. Do you agree with Clare or Kiran? Explain your thinking.

Answer 1

Firstly, we need to examine the validity of their claims

Clare claims that "$5x+2 = 20$ has the same solution as $5(5x+2) = 60$," and Kiran also claims that "$5x+2=12$ has the same solution as $5(5x+2)=60$."

Let's check Claire's claim :

Solution of $5x + 2 = 20$

`5x &=& 18\\ x &=& (18)/(5)`

Solution of $5(5x+2) = 60$

`5x + 2 &=& (60)/(5)\\ 5x + 2 &=& 12 \\ 5x &=& 10 \\ x &=& 2`

The solution of each equation is different (inequal). Therefore Clare is wrong, hence I disagree with her.

Let's check Kiran's :

Solution of $5x + 2 = 12$

`5x &=& 10\\ x &=& 2`

Solution of $5(5x+2) = 60$

`5x + 2 &=& (60)/(5)\\ 5x + 2 &=& 12 \\ 5x &=& 10 \\ x &=& 2`

The solution of each equation is the same (equal). Therefore Kiran is correct, hence I agree with her.