Representing solutions of linear inequalities in one variable on a number line

Which solution set matches the graph provided?

• x < 2

• x > 2

• x > 2

• x < 2

Write the absolute value inequality represented in the graph.

• $f\left(x\right)>\left|x-1\right|+3$

• $f\left(x\right)<\left|x-1\right|+3$

• $f\left(x\right)<\left|x+1\right|+3$

• $f\left(x\right)\le\left|x+1\right|-3$

The following number-line can be represented as:

• $\left|x-6\right|<-1$

• $\left|x+6\right|<-1$

• $\left|x-\frac{7}{2}\right|<\frac{5}{2}$

• $\left|x+\frac{7}{2}\right|<\frac{5}{2}$

Which graph represents the solution to the absolute-value inequality:

I 2x - 11 I < 21

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Answer explanation

Remember what sort of graph < means for absolute-value.

Graph.
 $y\le\left|x+3\right|-5$  

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Solve for "x":
 $\left|2x-9\right|<11$  

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Solve the absolute Value inequality and graph. 

• A
• B
• C
• D

Identify the absolute value inequality that would generate the given graph.

•  $\left|x+12\right|>5$  

•  $\left|x+12\right|\ge5$  

•  $\left|x+12\right|<5$  

•  $\left|x+12\right|\le5$  

What is the absolute value of the submarine if it is 1200 below zero?

• -1200

• 1200

• 5000

• +1200

What is the correct interval notation for the graph?

• (-2,5)

• (-∞,-2)⋃(5,∞)

• [-2,5]

• (-∞,-2]∪[5,∞)