Q51. - Algebra 1

Question

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

$14+x=21$

Step-by-Step Solution

Answer

The solution of the equation $14+x=21$ is $x=7$.

Step 1. Given information.

We have an equation $14+x=21$ 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 $14+x=21$

         $$\begin{gathered} 14+1=21 \\ \Rightarrow 15\ne 21 \end{gathered}$$

  $x=1$ is not solution 

Substitute $x=3$ in the equation $14+x=21$

        $$\begin{gathered} 14+3=21 \\ \Rightarrow 17\ne 21 \end{gathered}$$

  $x=3$ is not solution 

Substitute $x=5$ in the equation $14+x=21$

       $$\begin{gathered} 14+5=21 \\ \Rightarrow 19\ne 21 \end{gathered}$$

  $x=5$ is not solution 

Substitute $x=9$ in the equation $14+x=21$

        $$\begin{gathered} 14+9=21 \\ \Rightarrow 23\ne 21 \end{gathered}$$

  $x=9$ is not solution 

Substitute $x=7$ in the equation $14+x=21$

    $$\begin{gathered} 14+7=21 \\ \Rightarrow 21=21 \end{gathered}$$

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