The sentence
‘$\,x = \pm 3\,$’
is a convenient shorthand for
‘$\,x = 3\ \text{ or }\ x = 3\,$’ .
Sentences like this are important when solving absolute value equations.
The sentence ‘$\,x = \pm 3\,$’ is read aloud as
‘$\,x\,$ is plus or minus three’
or ‘$\,x\,$ equals plus or minus three’ .
This web exercise gives you practice working with ‘plus or minus’ sentences.
When working with sentences involving plus or minus ($\,\pm\,$), you have two choices:
The examples below illustrate both approaches.$2x  1 = \pm 5$  (original sentence) 
$2x  1 = 5\ \text{ or }\ 2x  1 = 5$  (expand the shorthand notation) 
$2x = 6\ \text{ or }\ 2x = 4$  (add $\,1\,$ to both sides of both equations) 
$x = 3\ \text{ or }\ x = 2$  (divide both sides of both equations by $\,2\,$) 
$2x  1 = \pm 5$  (original sentence) 
$2x = \pm 5 + 1$  (add $\,1\,$ to both sides—you cannot simplify anything on the right!) 
$\displaystyle x = \frac{\pm 5 + 1}{2}$  (divide both sides by $\,2\,$) 
$\displaystyle x = \frac{5 + 1}{2}\ \text{ or }\ x = \frac{5 + 1}{2}$  (expand the shorthand; you can probably skip this step and jump right to the next one) 
$\displaystyle x = 3\ \text{ or }\ x = 2$  (simplify) 
The method you choose to use is entirely up to you!
Solve the given absolute value sentence.
Write the result in the most conventional way.
For more advanced students, a graph is displayed.
For example, the sentence $\,2x  1 = \pm 5\,$
is optionally accompanied by the
graph of $\,y = 2x  1\,$ (the left side of the equation, dashed green)
and the graph of
$\,y = \pm 5\,$ (the right side of the equation, solid purple).
In this example, you are finding the values of $\,x\,$ where the green
graph intersects the purple graph.
Click the “show/hide graph” button if you prefer not to see the graph.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
