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Q15.

Expert-verifiedFound in: Page 179

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 $x=-11$.

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 $f\left(x\right)$.

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.

| $f\left(x\right)=11x+121$ | $f\left(x\right)$ | ( |

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

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

** **

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 $x=-11$.

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