Question

Kim is solving the following linear equation:
12 + 5x - 8 = 9x + 7 - 4x
Her final two steps are:
4 + 5x = 5x + 7 4 = 7

Select the statement that correctly interprets Kim's solution.

The solution is the ordered pair (4, 7). The solution is the ordered pair (4, 7).

There is no solution because 4 = 7 is a false statement.

There is no solution because 4 = 7 is a false statement.

There are infinitely many solutions because there is no x in the final equation.

There are infinitely many solutions because there is no , x, in the final equation.

The solution is x = 0

Answer 1

Solution :

Given linear equation :

12 + 5x - 8 = 9x + 7 - 4x

Grouping Similar Terms together ;

=> ( 12 - 8 ) + 5x = ( 9 x - 4x ) + 7

Simplifying :

=> 4 + 5x = 5x + 7

So, his second step is correct .

Proceeding :

=> 4 + 5x = 5x + 7

=> ( 5x - 5 x ) = ( 7 - 4 )

=> 0 • x = 3

BUT , 0 × anything = 0

So, there is 0 on the LHS and 3 on the RHS

0 ≠ 3

So, there is no solution .

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Answer 2

Given :

12+5x-8 = 9x + 7 -4x

Take the similar terms ;

=> (12-8)+5x=(9x-4x)+7

Now , simpliying ;

• 4+5x = 5x + 7 ( As the 2nd step is correct )

Now , solving it we get :

• 4+5x = 5x + 7
• (5x - 5x) = (7-4)
• 0×3 = 3

We know that anything multiple with 0 the value is always 0 .

Keeping , 0 on the LHS side and 3 at the RHS side we get ; 0 not equal to 3 .

Hence , it is not a solution .

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- @ClusterBoy