Q1A. - Algebra 1

Question

Determine the solution set for the following equation if the replacement set is $\left\{0,1,2,3\right\}$:

$\mathbf{8}\mathit{m}\mathbf{-}\mathbf{7}\mathbf{=}\mathbf{17}$

Step-by-Step Solution

Answer

The solution set of the equation $8m-7=17$ is $\left\{3\right\}$.

Step 1. Given information.

The equation is $8m-7=17$ and the replacement set is $\left\{0,1,2,3\right\}$.

Step 2. Write the concept.

If $x=a$, where a is any real number, is a solution of the equation $x+b=c$. Then, $x=a$ satisfies the equation. Here b and c are also any real numbers.

Step 3. Find the solution set.

Substitute the values from the replacement set one by one in the equation $8m-7=17$.

At $m=0$,

$\begin{array}{l} 8m-7=17\\ 8\left(0\right)-7=17\\ -7\ne 17\end{array}$

So, $m=0$ is not a solution to the equation $8m-7=17$.

At $m=1$,

$\begin{array}{l} 8m-7=17\\ 8\left(1\right)-7=17\\ 1\ne 17\end{array}$

So, $m=1$ is not a solution to the equation $8m-7=17$.

At $m=2$,

$\begin{array}{l} 8m-7=17\\ 8\left(2\right)-7=17\\ 9\ne 17\end{array}$

So, $m=2$ is not a solution to the equation $8m-7=17$.

At $m=3$,

$\begin{array}{l} 8m-7=17\\ 8\left(3\right)-7=17\\ 17=17\end{array}$

So, $m=3$ is a solution to the equation $8m-7=17$.

Therefore, the solution set is $\left\{3\right\}$.