Q55. - Algebra 1

Question

Find the solution of each equation if the replacement sets are $x:\left\{1,3,5,7,9\right\}$ and $y:\left\{6,8,10,12,14\right\}$

$2\left(x-1\right)=8$

Step-by-Step Solution

Answer

The solution of the equation $2\left(x-1\right)=8$ is $x=5$.

Step 1. Given information.

We have an equation $2\left(x-1\right)=8$ 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. Apply concept.

We substitute the values of $x$ in the given equation one by one and check which value of $x$ makes both the sides of the equation equal.

Which value of $x$ makes both the sides of the equation that is called the solution of the given equation.

Step 3. Calculation.

Substitute $x=1$ in the equation $2\left(x-1\right)=8$

         $$\begin{gathered} 2\left(1-1\right)=8 \\ \Rightarrow 2·1-2·1=8 \\ \Rightarrow 2-2=8 \\ \Rightarrow 0\ne 8 \end{gathered}$$

  $x=1$ is not solution 

Substitute $x=3$ in the equation $2\left(x-1\right)=8$

          $$\begin{gathered} 2\left(3-1\right)=8 \\ \Rightarrow 2·3-2·1=8 \\ \Rightarrow 6-2=8 \\ \Rightarrow 4\ne 8 \end{gathered}$$

  $x=3$ is not solution 

Substitute $x=5$ in the equation $2\left(x-1\right)=8$

        $$\begin{gathered} 2\left(5-1\right)=8 \\ \Rightarrow 2·5-2·1=8 \\ \Rightarrow 10-2=8 \\ \Rightarrow 8=8 \end{gathered}$$

  $x=5$ is a solution 

Substitute $x=9$ in the equation $2\left(x-1\right)=8$

         $$\begin{gathered} 2\left(9-1\right)=8 \\ \Rightarrow 2·9-2·1=8 \\ \Rightarrow 18-2=8 \\ \Rightarrow 16\ne 8 \end{gathered}$$

  $x=9$ is not solution 

Substitute $x=7$ in the equation $2\left(x-1\right)8$

        $$\begin{gathered} 2\left(7-1\right)=8 \\ \Rightarrow 2·7-2·1=8 \\ \Rightarrow 14-2=8 \\ \Rightarrow 12\ne 8 \end{gathered}$$

  $x=7$ is not a solution

Hence, the $x=5$ is the solution of the given equation.