Q53. - Algebra 1

Question

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

$3x-11=16$

Step-by-Step Solution

Answer

The solution of the equation $3x-11=16$ is $x=9$.

Step 1. Given information.

We have an equation $3x-11=16$ 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 $x=11$ in the equation $3x-11=16$

         $$\begin{gathered} 3·1-11=16 \\ \Rightarrow 3-11=16 \\ \Rightarrow -8\ne 16 \end{gathered}$$

  $x=1$ is not solution 

Substitute $x=3$ in the equation $3x-11=16$

         $$\begin{gathered} 3·3-11=16 \\ \Rightarrow 9-11=16 \\ \Rightarrow -2\ne 16 \end{gathered}$$

  $x=3$ is not solution 

Substitute $x=5$ in the equation $3x-11=16$

         $$\begin{gathered} 3·5-11=16 \\ \Rightarrow 15-11=16 \\ \Rightarrow 4\ne 16 \end{gathered}$$

  $x=5$ is not solution 

Substitute $x=9$ in the equation $3x-11=16$

         $$\begin{gathered} 3·9-11=16 \\ \Rightarrow 27-11=16 \\ \Rightarrow 16=16 \end{gathered}$$

  $x=9$ is a solution

Substitute $x=7$ in the equation $3x-11=16$

         $$\begin{gathered} 3·7-11=16 \\ \Rightarrow 21-11=16 \\ \Rightarrow 10\ne 16 \end{gathered}$$

  $x=7$ is not a solution

Hence, the $x=9$ is the solution of the given equation.