# How do you graph and solve | 5 x + 5 | = 0?

Dec 2, 2015

$x = \left(- 1\right)$
I have no idea how you would graph this context other than a line parallel to the y-axis that passes through $x = - 1$ ?????

#### Explanation:

The value on the right is zero. So what is on the left has to have the same value as zero.

So $| 5 x + 5 | \equiv 0$

As far as I can see $x$ can only have 1 value and that is $\left(- 1\right)$
This is because $| 0 | = 0$

and $5 \times \left(- 1\right) + 5 = 0$

so $| 5 \times \left(- 1\right) + 5 | = 0$

Dec 2, 2015

$x = - 1$
The graph should be v-shaped.

#### Explanation:

Solving the equation for $x$.

$\left\mid 5 x + 5 \right\mid = 0$

Remove the absolute value.

$5 x + 5 = 0$

Subtract $5$ from both sides.

$5 x = - 5$

Divide both sides by $5$.

$x = \frac{- 5}{5}$

$x = - 1$

Graphing the Equation

$\left\mid 5 x + 5 \right\mid = 0$

Since the expression inside the absolute value bars can be positive or negative, and we need to graph it, we need to substitute $y$ for $0$ so we can get points to plot on the graph.

$\left\mid 5 x + 5 \right\mid = y$

Now we need to substitute positive and negative values for $x$ and solve for $y$.

Table of Points
$x = - 3 ,$ $y = 10$
$x = - 2 ,$ $y = 5$
$x = - 1 ,$ $y = 0$
$x = 0 ,$ $y = 5$
$x = 1 ,$ $y = 10$
$x = 2 ,$ $y = 15$
$x = 3 ,$ $y = 20$

Plot the points, then connect the dots. You should have a v-shaped graph.

graph{y=abs(5x+5) [-16.42, 15.6, -2.69, 13.33]}