Q13. - Algebra 1

Question

Find the solution of the equation $3x-9=12$ if the replacement sets are $x:\left\{1,3,5,7,9\right\}$ and $y:\left\{2,4,6,8,10\right\}$.

Step-by-Step Solution

Answer

The solution of the equation $3x-9=12$ is $x=7$.

Step 1. Given information.

We have an equation $3x-9=12$ and a set $x:\left\{1,3,5,7,9\right\}$

To find the solution of the given equation at every value of x.

Step 2. Calculation.

Substitute $x=1$ in the equation $3x-9=12$

         $3\times 1-9=12$

     $\Rightarrow 3-9=12$

     $\Rightarrow -6\ne 12$

$x=1$ is not the solution of the given equation.

Substitute $x=3$ in the equation $3x-9=12$

        $3\times 3-9=12$

     $\Rightarrow 9-9=12$

     $\Rightarrow 0\ne 12$

$x=3$ is not the solution of the given equation.

Substitute $x=5$ in the equation $3x-9=12$

       $3\times 5-9=12$

     $\Rightarrow 15-9=12$

     $\Rightarrow 6\ne 12$

$x=5$ is not the solution of the given equation.

Substitute  in the equation $3x-9=12$

        $3\times 9-9=12$

     $\Rightarrow 27-9=12$

     $\Rightarrow 18\ne 12$

$x=9$ is not the solution of the given equation.

Step 3. Conclusion.

Substitute $x=7$ in the equation $3x-9=12$

     $3\times 7-9=12$

  $\Rightarrow 21-9=12$

 $\Rightarrow 12=12$

Hence, the $x=7$ is the solution of the given equation.