Q15. - Algebra 1

Question

Solve each equation by graphing.

$118+11x=-3$

Step-by-Step Solution

Answer

The solution of equation $118+11x=-3$ is $x=-11$.

Step 1. State the Concept of solving an equation by graphing.

A linear function is a function whose graph is a straight line. The solution or root of an equation is any value that makes the equation true. A linear equation has at most one root. Root of an equation can be calculated by graphing the related function. To write the related function for an equation, replace 0 with $f\left(x\right)$.

Step 2. Write the related function.

Since the equation is given to be $118+11x=-3$,

$$\begin{gathered} 118+11x+3=-3+3 \\ 11x+121=0 \end{gathered}$$ 

therefore, its related function will be $11x+121=f\left(x\right)$. To graph the function, make a table.

 

x	$f\left(x\right)=11x+121$	$f\left(x\right)$	(x, $f\left(x\right)$)
$-11$	$\begin{array}{c}f\left(-11\right)=11\left(-11\right)+121\\ =0\end{array}$	0	$\left(-11,0\right)$
0	$\begin{array}{c}f\left(0\right)=11\left(0\right)+121\\ =121\end{array}$	121	$\left(0,121\right)$

 

Step 3. Plot the function.

Graph the equation $11x+121=f\left(x\right)$ by plotting the values from the table and get:

The graph intersects the x-axis at $-11$. So, the solution is $x=-11$.