Absolute Value Inequalities

A(n) ________________ is an inequality that contains an absolute value expression.

• absolute value inequality

• expressive inequality

• equal inequality

• complex inequality

Recall that absolute value describes the __________________ from zero that a number is on the number line.

• distance

• mode

• arithmetic mean

• median

Tags

CCSS.6.NS.C.7

The absolute value of an expression must be greater than or equal to zero.

• always

• sometimes

• never

The absolute value of an expression cannot be less than zero.

• always

• sometimes

• never

 $\left|x\ -\ 5\right|\ \le\ 10\$  

•  $-\ 5\ \le x\ \le15\$  

• none of these 

•  $x\ >\ -\ 5\ OR\ x\ <15\$  

•  $-15\ \le\ x\ \le\ 15\$  

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

 $\left|\ 2x\ -\ 7\ \right|\ \ge\ -\ 11\$  

• all real numbers 

• no solution 

•  $x\ \ge\ 5\ OR\ x\ \le-19$  

•  $-12\ \le\ x\ \ \le12$  

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

 $\left|2x\ +\ 2\right|\ <\ -\ 8\$  

• no solution 

• all real numbers 

•  $-5\ \le\ x\ \le\ 5\$  

•  $x\ \le\ -\ 5\ OR\ x\ \ge\ 5\$  

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

 $\left|4x\ -\ 2\ \right|\ \ge\ -\ 6\$  

Can you determine the solution of the given inequality without solving?

• Yes, the absolute value must be positive; all values will be greater than negative six. The answer is all real numbers. 

• Yes, the answer is no solution. 

• No, the inequality will need to be divided into an AND or and OR compound inequality. 

• No, their is not enough information to complete this problem. 

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

TRUE or FALSE:

A compound inequality with the word 'and' can be written as a single inequality. For example, - 9 < x < 9

• True

• False

Tags

CCSS.HSA.REI.B.3

 $3\ \left|x\ +\ 1\ \right|\ -\ 7\ \ge\ -\ 1\$  

• no solution 

• all real numbers 

•  $x\ \le\ -\ 3\ OR\ x\ \ge1$  

•  $-\ 1\ \le\ x\ \le3\$  

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1