# How do you solve 2x+22=0 by graphing?

Jul 17, 2018

#### Answer:

Plot the graph of $\left(2 x + 22\right)$.
The solution is the value of $x$ where the line crosses the $x$ axis.

#### Explanation:

It is very easy to solve this by using algebra, but if you need to solve it by graphing then:

Plot the graph of $\left(2 x + 22\right)$.
The solution is the value of $x$ where 2$x$+22 = 0 (i.e. where the line crosses the $x$ axis).

You can do this with a graphic calculator or computer, or you can do it on paper as follows:

Put values for $x$ into the left hand side of the eqn
($2 x + 22$) ....(you should recognize this as a straight line)

and plot them as the $y$ value on a graph

e.g.
if $x$ = 0, $y = \left(2 \cdot 0\right) + 22 = 22$ so plot the point (0,22)
if $x$ = 4, $y = \left(2 \cdot 4\right) + 22 = 30$ so plot the point (4,30)
if $x$ = -6, $y = \left(2 \cdot - 6\right) + 22 = 10$ so plot the point (-6,10)

Draw a straight line through these points:
graph{2x+22 [-41.3, 38.7, -5.58, 34.42]}

The line shows all the values of $2 x + 22$ (read on $y$ axis) for all values of $x$ ($x$ axis)

We are interested in the value of $x$ when $2 x + 22 = 0$, so read the value of $x$ at $y = 0$ (where the line crosses the $x$ axis).

Looks like it's $x = - 11$

(We can check this by using $x = - 11$ in the expression 2$x$+22 and verifying that it is equal to 0 for this value of $x$)

$2 \cdot - 11 + 22 = - 22 + 22 = 0$

The plot of $x = - 11$ on a graph is a vertical line through x=-11
graph{-1000x-11000 [-41.3, 38.7, -5.58, 34.42]}