"And" or "Or" Inequalities and Equations

"And" or "Or" Inequalities and Equations

Algebra I

Declarative Compound Sentences

• When two declarations in a sentence are separated by "and," both declarations must be true for the entire statement to be true.

• When two declarations in a sentence are separated by "or," only one declaration must be true for the entire statement to be true.

• ***Both declarations can be true in "or" statements***

Multiple Choice

Mr. Jackson is a math and Spanish teacher.

• True

• False

Multiple Choice

Mr. Jackson is a math or Spanish teacher.

• True

• False

Multiple Choice

CJR is an elementary/middle school and has after school activities like lacrosse.

• True

• False

Multiple Choice

CJR has basketball or rugby.

• True

• False

"And" or "Or" Statements Also Work Mathematically

View the example image to the right along with the three examples on the next page.

True or False?

For the next two slides, determine whether the two-part declarative statements are true or false.

Multiple Choice

 $13+7=20$ and  $-3<3$   

• True

• False

Multiple Choice

 $6<4\ • 2$ or $11+2=9$  

• True

• False

Systems of Equations and Inequalities

More than one equation or inequality at once

Multiple Choice

Which two values make this system true? Hint: Solve each equation.

 $x+8=3$  OR  $x-6=2$  

• {5, 8}

• {-5, 8}

• {11, 8}

• {5, -4}

Multiple Choice

Solve the system. Hint: Solve each equation individually.

 $4x-9=0$  OR  $3x+5=2$  

• { $\frac{9}{4}$ ,  $\frac{7}{3}$  }

• {2, -1}

• {-1, $\frac{9}{4}$ }

• { $\frac{9}{4}$ , 1}

Multiple Choice

Solve the system.

 $x-6=1$  AND  $x+2=9$  

• {-7}

• {-7, 7}

• {7}

• {-5, 11}

Multiple Choice

Solve the system. HINT: Remember what "and" indicates.

 $2w-8=10$  AND  $w>9$  

• No Solution (Empty Set)

• {9}

• {10}

• {9, 10}

Previous Question

Please look at the image to the right to recap the previous question.

The Next Two Slides Are Examples

There will be questions after the examples.

Multiple Choice

Which graph represents the following compound sentence?

 $x>-2$  or  $x=-2$  

Multiple Choice

Which compound sentence matches the inequality?

•  $x=2$  or $x\ge6$  
  

•  $x=2$  or $x=6$  
  

•  $x=2$  or $x<6$  

•  $x=2$  or $x>6$  

Multiple Choice

Which compound sentence matches the inequality?

•  $x\le-5$  or $x\ge2$  
  

•  $x\le-5$  or $x>2$  
  

•  $x\ge-5$  or $x\le2$  

•  $x<-5$  or $x\ge2$  

Multiple Choice

In mathematical sentences, like in English sentences, a compound sentence separated by AND is true if _______ clauses are true.

• both

• at least one of the

Multiple Choice

In mathematical sentences, like in English sentences, a compound sentence separated by OR is true if _______ clauses are true.

• both

• at least one of the

Open Ended

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