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Q15.

Expert-verified
Found in: Page 179

### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

# Solve each equation by graphing.$118+11x=-3$

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

See the step by step solution

## 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 $118+11x=-3$,

$118+11x+3=-3+3\phantom{\rule{0ex}{0ex}}11x+121=0$

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 $x=-11$.