﻿ Solving Sentences Involving "Plus or Minus"
SOLVING SENTENCES INVOLVING ‘PLUS OR MINUS’
• PRACTICE (online exercises and printable worksheets)
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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:

• break into an ‘or’ sentence immediately
• wait until the last step to break into an ‘or’ sentence
The examples below illustrate both approaches.

EXAMPLE:   Break into an ‘or’ sentence immediately
Solve: $2x - 1 = \pm 5$
Solution:
Be sure to write a nice, clean list of equivalent sentences.
 $2x - 1 = \pm 5$ (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 $\,2\,$)
EXAMPLE:   Wait until the last step to break into an ‘or’ sentence
Solve: $2x - 1 = \pm 5$
Solution:
 $2x - 1 = \pm 5$ (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!

Master the ideas from this section

When you're done practicing, move on to:
Solving Absolute Value Equations

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: